The step-stress model is becoming quite popular for analyzing lifetime data obtained from accelerated life testing experiments. In the usual step-stress experiment, stress levels are allowed to change at each step to get rapid failure of the experimental units. The simple step-stress model under different censoring schemes based on Weibull lifetimes is considered in this paper. It is assumed that the lifetime distributions of the experimental units have different scale parameters at different stress levels, but they have the same shape parameter. Moreover, it is assumed that the lifetimes follow the Khamis-Higgins model. It is further assumed that, as the stress level increases, the scale parameter also increases. We provide Bayesian inference of the unknown parameters of the Weibull distribution under this order restriction on the scale parameters. Monte Carlo simulations have been performed to see the effectiveness of the proposed method, and a data set has been analyzed for illustrative purposes.

This paper considers different algorithms for solving the color constancy problem in the block DCT domain. New algorithms in this domain have been proposed by exploiting the advantage of smaller data size and the better chromatic separation of Y-Cb-Cr color space (as used in the JPEG standard) against the R-G-B color space of the spatial domain. These make them faster and less memory intensive compared to their equivalent ones in the spatial domain without any significant degradation of the quality of the results.

This paper presents a new efficient technique for color enhancement in the compressed domain. In the proposed technique the enhancement computation is performed in three steps, namely, adjustment of dynamic range of brightness values, preservation of local contrast and preservation of color with all computations involving scaling of the DCT coefficients. Further special care has been taken for reducing the blocking artifacts. The proposed algorithm provide better performances compared to some of the existing techniques in the compressed domain.

This paper presents a new technique for color enhancement in the compressed domain. The proposed technique is simple but more effective than some of the existing techniques reported earlier. The novelty lies in this case in its treatment of the chromatic components, while previous techniques treated only the luminance component. The results of all previous techniques along with that of the proposed one are compared with respect to those obtained by applying a spatial domain color enhancement technique that appears to provide very good enhancement. The proposed technique, computationally more efficient than the spatial domain based method, is found to provide better enhancement compared to other compressed domain based approaches.

With the growing surge of biological measurements, the problem of integrating and analyzing different types of genomic measurements has become an immediate challenge for elucidating events at the molecular level. In order to address the problem of integrating different data types, we present a framework that locates variation patterns in two biological inputs based on the generalized singular value decomposition (GSVD). In this work, we jointly examine gene expression and copy number data and iteratively project the data on different decomposition directions defined by the projection angle theta in the GSVD. With the proper choice of theta, we locate similar and dissimilar patterns of variation between both data types. We discuss the properties of our algorithm using simulated data and conduct a case study with biologically verified results. Ultimately, we demonstrate the efficacy of our method on two genome-wide breast cancer studies to identify genes with large variation in expression and copy number across numerous cell line and tumor samples. Our method identifies genes that are statistically significant in both input measurements. The proposed method is useful for a wide variety of joint copy number and expression-based studies. Supplementary information is available online, including software implementations and experimental data.

An error concealment using data hiding (ECDH) technique is proposed to improve the end user perceptual quality of videos that are affected by transmission defects. A 2/spl times/2 set of coefficients from each block of block-based 2D DCT of the video frame is encoded using DPCM and embedded in the frame itself using a low gain spread spectrum watermarking technique. The DPCM bit stream is ordered into a binary block-image, which is approximately 4 times smaller than the video frame, and embedded in the frame's mid-frequencies. At the receiver, the extracted DPCM bits are lexicographically ordered and a reference is reconstructed for error concealing the channel loss affected video frame. The technique is closely compared with a similar approach which embeds halftoned bits of a low resolution version of the video frame in itself. Also, a comparison is done when the DPCM encoded bits are transmitted as side information through the channel rather than as embedded data. Experimental results show that the technique that uses DPCM bit stream embedding is more effective than the other two ECDH techniques as well as most other error concealment algorithms.

Synthetic artifacts offer many advantages for experimental research on video quality because of the degree of control that the researchers have with respect to the amplitude, distribution, and mixture of artifacts. We have developed algorithms for synthetically generating four types of artifacts commonly found in digital videos: blockiness, blurriness, noisiness, and ringing. In this paper, we inserted these artifacts in short video sequences and performed a psychophysical experiment where we measured the probability of detection and the mean annoyance values of these artifacts as a function of their total squared error (TSE). The results show that, although the different artifacts looked different and affected the videos differently, there is no consistent difference between either their visibility thresholds or mid-annoyance TSE. Mid-annoyance values are positively correlated with the visibility threshold, and the relation can be described by a linear function.

In this work, the detector performance of a watermark-based error concealment (WEC) system proposed in C.B. Adsumilli is mathematically analyzed. The spread spectrum based WEC algorithm embeds a low resolution version of an image in itself during encoding. At the receiver, this embedded watermark is extracted and used as a reference to conceal the transmission losses in the reconstructed image. For the application of error concealment, the detector modelling varies from the conventional watermark detectors due to the fact that we use a full frame DCT to embed the watermark data and vary the strength of the watermark in accordance with the embedding coefficients to reduce the standard deviation of the resulting distribution. We further approximate the full frame DCT coefficients to follow a generalized Gaussian distribution (GGD) like in the case of modelling block-based DCT coefficients and consequently, we provide a comparison between the performance of this system and conventional block-based embedding strategies for various packet loss probabilities. Both analytical and simulation results show that our system of full frame DCT embedding is more effective for error concealment in detecting the embedded bits with lesser probability of error.

In this paper we present a no-reference video quality metric based on individual measurements of three artifacts: blockiness, blurriness, and noisiness. The set of artifact metrics (physical strength measurements) was designed to be simple enough to be used in real-time applications. The metrics are tested using a proposed procedure that uses synthetic artifacts and subjective data obtained from previous experiments. The technique has the advantage of allowing us to test each metric on videos which contain only the desired artifact signal or a combination of artifact signals. Models for the overall annoyance based on a combination of the artifact metrics using both a Minkowski metric and a linear model are developed. Both models present a very good correlation with the data and show no statistical difference in their performances.

In this letter, we propose results of distribution tests that indicate that for many natural images, the statistics of the discrete cosine transform (DCT) coefficients are best approximated by a generalized gamma function (G/spl Gamma/F), which includes the conventional Gaussian, Laplacian, and gamma probability density functions. The major parameter of the G/spl Gamma/F is estimated according to the maximum likelihood (ML) principle. Experimental results on a number of /spl chi//sup 2/ tests indicate that the G/spl Gamma/F can be used effectively for modeling the DCT coefficients compared to the conventional Laplacian and generalized Gaussian function (GGF).

A robust error concealment scheme using data hiding which aims at achieving high perceptual quality of images and video at the end-user despite channel losses is proposed. The scheme involves embedding a low-resolution version of each image or video frame into itself using spread-spectrum watermarking, extracting the embedded watermark from the received video frame, and using it as a reference for reconstruction of the parent image or frame, thus detecting and concealing the transmission errors. Dithering techniques have been used to obtain a binary watermark from the low-resolution version of the image/video frame. Multiple copies of the dithered watermark are embedded in frequencies in a specific range to make it more robust to channel errors. It is shown experimentally that, based on the frequency selection and scaling factor variation, a high-quality watermark can be extracted from a low-quality lossy received image/video frame. Furthermore, the proposed technique is compared to its two-part variant where the low-resolution version is encoded and transmitted as side information instead of embedding it. Simulation results show that the proposed concealment technique using data hiding outperforms existing approaches in improving the perceptual quality, especially in the case of higher loss probabilities.

One approach for studying digital video impairments is to work with synthetic artifacts which look like real impairments, yet are simpler, purer and easier to describe. We have created synthetic ringing and blurring and inserted them in short video sequences. In a psychophysical experiment, we measured the probability of detection and the annoyance value of these artifacts as a function of their total squared error. Although ringing occurs only near edges and blurring can occur over wide areas of the images, there is no consistent difference between either the thresholds or mid-annoyance strengths. There are, on the other hand, interactions between the specific video and artifact type in the determination of these values. Mid-annoyance strength was found to be highly correlated with threshold. Also, we combined ringing and blurring to produce mixed artifacts. Their thresholds and mid-annoyance strengths tend to be intermediate between those of the individual artifacts. Their annoyance value is well predicted by a weighted sum of the annoyance values for blurring and ringing with weights of approximately 0.6 and 0.4, respectively.

A multilayer perceptron (MLP) can be used to implement a vector quantizer (VQ) under severe constraints in the computational complexity allowed. Such constraints are typical in applications such as focal-plane image compression, in which we are interested in eliminating the analog-to-digital (A/D) converters and mapping the analog data directly into a compressed bit stream, to save energy and silicon area. We compare a nonlinear MLP called the kernel lattice vector quantizer (KLVQ) and a clustering MLP known as the cluster-detection-and-labeling (CDL) network, with regard to their hardware requirements. We show that for similar rate-distortion performances, the KLVQ has complexity smaller than that of the CDL network.

A new structure for the realization of a comb decimation filter with a sharpened magnitude response is advanced. The proposed structure consists of two main sections: a comb section and a sharpening comb section with the latter section operating at a lower rate than the high input rate. Using a polyphase decomposition, the sub-filters of the first section can also be operated at this lower rate. The improved magnitude response has been obtained by using the filter sharpening approach of J.F. Kaiser and R.W. Hamming (see IEEE Trans. on Acoustics, Speech, and Sig. Process., vol.ASSP25, p.415-22, 1977). The proposed filter has much less passband droop and better attenuation than the equivalent comb filter.

This paper describes the results of a series of subjective experiments that investigated the annoyance caused by the most common artifacts present in segmented video sequences. Various types of artifacts were inserted into a reference segmented video, considered as ideal, and shown to our test subjects. The artifacts varied in their location, size, appearance and duration. Annoyance of segmentation artifacts are found to be tied up with their intrinsic characteristics (e.g., size, position) but only weakly related to the video content. The results identify the characteristics that should be taken into account in the design of a perceptually driven objective metric.

BACKGROUND: Microarray data normalization is an important step for obtaining data that are reliable and usable for subsequent analysis. One of the most commonly utilized normalization techniques is the locally weighted scatterplot smoothing (LOWESS) algorithm. However, a much overlooked concern with the LOWESS normalization strategy deals with choosing the appropriate parameters. Parameters are usually chosen arbitrarily, which may reduce the efficiency of the normalization and result in non-optimally normalized data. Thus, there is a need to explore LOWESS parameter selection in greater detail. RESULTS AND DISCUSSION: In this work, we discuss how to choose parameters for the LOWESS method. Moreover, we present an optimization approach for obtaining the fraction of data points utilized in the local regression and analyze results for local print-tip normalization. The optimization procedure determines the bandwidth parameter for the local regression by minimizing a cost function that represents the mean-squared difference between the LOWESS estimates and the normalization reference level. We demonstrate the utility of the systematic parameter selection using two publicly available data sets. The first data set consists of three self versus self hybridizations, which allow for a quantitative study of the optimization method. The second data set contains a collection of DNA microarray data from a breast cancer study utilizing four breast cancer cell lines. Our results show that different parameter choices for the bandwidth window yield dramatically different calibration results in both studies. CONCLUSIONS: Results derived from the self versus self experiment indicate that the proposed optimization approach is a plausible solution for estimating the LOWESS parameters, while results from the breast cancer experiment show that the optimization procedure is readily applicable to real-life microarray data normalization. In summary, the systematic approach to obtain critical parameters in the LOWESS technique is likely to produce data that optimally meets assumptions made in the data preprocessing step and thereby makes studies utilizing the LOWESS method unambiguous and easier to repeat.

This paper advances a new framework for chromatic filtering of color images. The chromatic content of a color image is encoded in the CIE u'v' chromaticity coordinates whereas the achromatic content is encoded as CIE Y tristimulus value. Within the u'v' chromaticity diagram, colors are added according to the well-known center of gravity law of additive color mixtures, which is generalized here into a nonlinear filtering scheme for processing the two chromatic signals u' and v'. The achromatic channel Y can be processed with traditional filtering schemes, either linear or nonlinear, depending on the specific task at hand. The most interesting characteristics of the new filtering scheme are: 1) the elimination of color smearing effects along edges between bright and dark areas; 2) the possibility of processing chromatic components in a noniterative fashion through linear convolution operations; and 3) the consequent amenability to computationally efficient implementations with fast Fourier transform. The paper includes several examples with both synthetic and real images where the performance of the new filtering method is compared with that of other color image processing algorithms.

A novel hybrid scheme with constrained unequal error protection (UEP) and data hiding is proposed; it maximizes the perceptual quality of the video at the end user to compensate for the effects of channel losses. The technique involves: (1) implementing a forcing function which weighs the objective perceptual quality of the video frame based on a hidden mark signal to give optimum protection level in the packet; (2) utilizing a data hiding mechanism to embed second level wavelet approximation coefficients of the frame in itself. An optimum UEP in the transmitted packets is sought using a constrained optimization approach. Simulation results show that the proposed technique outperforms existing non-adaptive error concealment approaches in improving the perceptual quality, especially for higher loss probabilities.

We propose an efficient sharpening of a CIC decimation filter for an even decimation factor. The proposed structure consists of two main sections: a section composed of a cascade of the first-order moving average filters, and a sharpening filter section. The proposed decomposition scheme allows a sharpening section to operate at half of the input rate. In addition, the sharpened CIC filter is of length that is half of that of the original CIC filter. With the aid of the polyphase decomposition, the polyphase subfilters of the first section can also be operated at the half of the input rate.

This work proposes a multilayer perception (MLP) method to perform direct mapping from an analog image block into a vector index, i.e. implement vector quantization (VQ) without the need for carrying out first an analog-to-digital (A/D) conversion of each analog sample. The design focuses on an analog hardware implementation and is based on observing that the use of a careful binary index assignment causes hyperplanes associated with the formation of the same bit at the MLP output to have similar spatial orientation. Experimental results show that, for the same rate-distortion performance, MLPs can be implemented with less than half the computational complexity of the Kohonen self-organizing map (KSOM) approaches advanced earlier.

Consumer digital color cameras use a single sensor with a color filter array to capture images. The captured data is first interpolated into a full color image, which is then compressed in many applications. The color interpolation process before compression introduces redundancy in the data. This paper outlines transformation methods before compression that remove this redundancy. The transformations described, maintain the same data size as the sensor data. The transformed data is compressed by JPEG to ensure retention of system simplicity by using standard technology and algorithms. Experiments demonstrate that substantial improvement in image quality is achievable using the proposed methods.

In this paper, we create synthetic artifacts that are perceived to be predominantly blocky, blurry or noisy. We present them alone or in various combinations and have subjects rate the perceived strength of each artifact and the overall annoyance of the combined artifacts. We found that a simple linear model with no interactions predicted how the perceived artifacts combine to determine overall annoyance. The estimated coefficients indicate that, when the artifacts are equated in perceived strength, blurriness contributes the most to annoyance followed by noise and then blockiness, although the relative weights of blockiness and noise vary with the video content.

A novel billing mechanism is presented in this paper to provide telecommunication service users and advertisers with an effective billing mechanism based on the actual amount of advertisement data being transmitted/displayed. Experimental results show the effectiveness of the proposed system in terms of computational cost and performance.

The set partitioning in hierarchical trees (SPIHT) approach for still-image compression proposed by Said and Pearlman (1996) is one of the most efficient embedded monochrome image compression schemes known to date. The algorithm relies on a very efficient scanning and bit-allocation scheme for quantizing the coefficients obtained by a wavelet decomposition of an image. In this paper, we adopt this approach to scan groups (vectors) of wavelet coefficients, and use successive refinement vector quantization (VQ) techniques with staggered bit-allocation to quantize the groups at once. The scheme is named vector SPIHT (VSPIHT). We present discussions on possible models for the distributions of the coefficient vectors, and show how trained classified tree-multistage VQ techniques can be used to efficiently quantize them. Extensive coding results comparing VSPIHT to scalar SPIHT in the mean-squared-error sense, are presented for monochrome images. VSPIHT is found to yield superior performance for most images, especially those with high detail content. The method is also applied to color video coding, where a partially scalable bitstream is generated. We present the coding results on QCIF sequences as compared against H.263.

The recently introduced concept of warped discrete Fourier transform (WDFT) [2] is reviewed and its main properties are compared with that of their well-known DFT counterparts. A number of new applications, such as frequency estimation of noise-corrupted short length sinusoids, discrete multitone transmission, and oversampled nonuniform filter banks, are described. In addition, some important design issues, such as the sensitivity of computing the inverse WDFT, are included.

A comparison between an objective quality measure and the perceived mean annoyance values of watermarked videos is presented. A psychophysical experiment has been performed to measure the detection threshold and mean annoyance values of several watermarked videos, using two different marks. The results of this experiment were then compared with an objective quality measure, obtained through a tracing watermarking system. An estimation of the detection threshold of the watermarked videos was found.

This paper presents a new method for enhancing the quality of color images degraded by white Gaussian noise. It consists in a straightforward application of the filtering scheme proposed by Lucchese and Mitra (see Proc. of Int'l Conference on Image Processing (ICIP 2000), Vancouver, Canada, Sept. Canada, Sept. 2000, vol.III, p.500-503) which allows the separate processing of the chromatic and achromatic channels of a color image, respectively encoded by the CIE u'v' chromaticity coordinates and by the tristimulus value Y. The first two signals are smoothed with a Gaussian lowpass filter whereas the latter is processed by anisotropic diffusion. The example discussed shows the effectiveness of this new denoising algorithm.

We describe the results of a series of psychophysical experiments that investigated the relationships among defect visibility, content importance, and perceived impairment in digital video. Various types of controlled defects were inserted into normal video and shown to our test subjects. The defects varied in their strength, location, appearance, size, and duration. We measured three specific subjective quantities: the defect detection probability, the perceived impairment, and the content importance. Impairment was found to be tightly related to defect visibility but only weakly related to content importance.

We present a new framework for rate-distortion (R-D) analysis, where the coding rate R and distortion D are considered as functions of /spl rho/ which is the percentage of zeros among the quantized transform coefficients. Previously (see He, Z. et al., Int. Conf. Acoustics, Speech and Sig. Proc., 2001), we observed that, in transform coding of images and videos, the rate function R(/spl rho/) is approximately linear. Based on this linear rate model, a simple and unified rate control algorithm was proposed for all standard video coding systems, such as MPEG-2, H.263, and MPEG-4. We further develop a distortion model and an optimum bit allocation scheme in the /spl rho/ domain. This bit allocation scheme is applied to MPEG-4 video coding to allocate the available bits among different video objects. The bits target of each object is then achieved by our /spl rho/-domain rate control algorithm. When coupled with a macroblock classification scheme, the above bit allocation and rate control scheme can also be applied to other video coding systems, such as H.263, at the macroblock level. Our extensive experimental results show that the proposed algorithm controls the encoder bit rate very accurately and improves the video quality significantly (by up to 1.5 dB).

We show that, in any typical transform coding system, there is always a linear relationship between the coding bit rate R and the percentage of zeros among the quantized transform coefficients, denoted by /spl rho/. Based on Shannon's source coding theorem, a theoretical justification is provided for this linear source model. The physical meaning of the model parameter is also discussed. We show that it is directly related to the image content and is a measure of picture complexity. In video coding, we propose an adaptive estimation scheme to estimate this model parameter. Based on the linear source model and the adaptive estimation scheme, a unified rate control algorithm is proposed for various standard video coding systems, such as MPEG-2, H.263, and MPEG-4. Our extensive simulation results show that the proposed rate control outperforms other algorithms reported in the literature by providing much more accurate and robust rate control.

Resizing of digital images is needed in various applications, such as transmission of images over communication channels varying widely in their bandwidths, display at different resolutions depending on the resolution of a display device, etc. In this work, we propose a modification of a recently proposed elegant image resizing algorithm by Dugad and Ahuja (2001). We have also extended their approach and our modified versions to color images and studied their performance at different levels of compression for an image. Our proposed modified algorithms, in general, perform better than the earlier method in most cases. Though there is a marginal increase in the computation required in image-halving, the computation overhead of the proposed modification is higher compared to the Dugad-Ahuja algorithm in the case of doubling the images.

Lattice Vector quantization (LVQ) solves the complexity problem of LBG based vector quantizers, yielding very general codebooks. However, a single stage LVQ, when applied to high resolution quantization of a vector, may result in very large and unwieldy indices, making it unsuitable for applications requiring successive refinement. The goal of this work is to develop a unified framework for progressive uniform quantization of vectors without having to sacrifice the mean- squared-error advantage of lattice quantization. A successive refinement uniform vector quantization methodology is developed, where the codebooks in successive stages are all lattice codebooks, each in the shape of the Voronoi regions of the lattice at the previous stage. Such Voronoi shaped geometric lattice codebooks are named Voronoi lattice VQs (VLVQ). Measures of efficiency of successive refinement are developed based on the entropy of the indices transmitted by the VLVQs. Additionally, a constructive method for asymptotically optimal uniform quantization is developed using tree-structured subset VLVQs in conjunction with entropy coding. The methodology developed here essentially yields the optimal vector counterpart of scalar "bitplane-wise" refinement. Unfortunately it is not as trivial to implement as in the scalar case. Furthermore, the benefits of asymptotic optimality in tree-structured subset VLVQs remain elusive in practical nonasymptotic situations. Nevertheless, because scalar bitplane- wise refinement is extensively used in modern wavelet image coders, we have applied the VLVQ techniques to successively refine vectors of wavelet coefficients in the vector set-partitioning (VSPIHT) framework. The results are compared against SPIHT and the previous successive approximation wavelet vector quantization (SA-W-VQ) results of Sampson, da Silva and Ghanbari.

Recent research in the design of filter banks has shown that nonorthogonal filter banks can potentially provide higher coding gains over orthogonal filter banks. The use of non-orthogonal filter banks, however, poses a difficulty in the quantization of subband signals. The conventional nearest-neighbor (NN) encoding rule for the quantization of subband signals is no longer optimal. In this paper, we propose two schemes for the quantization of subband signals in non-orthogonal subband coders. An optimal scheme for quantization of subband signals is proposed first. The complexity of the optimal quantization scheme is shown to grow exponentially with the length of the synthesis filters, which motivates the development of low-complexity quantization schemes when the length of the filters in the synthesis filter bank is large. The second quantization technique uses an iterative method to quantize the subband signals such that the mean square error between the input and the reconstructed output signals is minimized.

The coding bit rate, R, is considered as a function of /spl rho/ which is the percentage of zeros among the quantized DCT (discrete cosine transform) coefficients. We discover that the rate function, R(/spl rho/), has some very interesting properties in the /spl rho/-domain. By introducing the new concepts of characteristic rate curves and rate curve decomposition, a novel framework for source modeling is proposed. Using the proposed source model, we can estimate the rate-quantization (R-Q) curve before quantization and coding with relative error less than 5%. Based on the estimated R-Q curve, the output bit rate of the video encoder can be accurately controlled. Our extensive simulation results show that the proposed algorithm outperforms TMN8 (see Ribas-Corbera, J. and Lei, S., IEEE Trans. on Circuits and Systems for Video Technology, vol.9, p.172-85, 1999) and VM7 (see Chiang, T. and Zhang, Y.-Q., IEEE Trans. on Circuits and Systems for Video Technology, vol.7, p.246-50, 1997) rate control algorithms by providing more accurate and robust rate control.

Let /spl rho/ be the percentage of zeros among the quantized transform coefficients. We discover that, in any typical video coding system, there is always a strictly linear relationship between /spl rho/ and the actual coding bit rate R. This linearity leads to a novel and unified source model for different types of source data and different coding systems, such as H.263, MPEG-2, and MPEG-4. The proposed linear source model is much simpler, but much more accurate than other source models reported in the literature. Based on this source model, a unified rate control algorithm is proposed for the above three video coding systems. Despite its extreme simplicity, the proposed algorithm outperforms other rate control algorithms by providing more accurate and robust rate control.

A new constrained storage VQ (CSVQ) structure based on linear transforms and translates of a common root codebook is proposed. The new VQ structure, named LT-CSVQ (linear translate CSVQ) acts as a building block for multistage VQ implementations (LT-CS-MSVQ), and significantly reduces storage requirements from that required in tree-multistage VQ implementations. LT-CS-MSVQ is most appropriate for medium rate multistage VQ implementations, and is applied to the previously proposed vector enhancement of Said and Pearlman's (1996) set partitioning in hierarchical trees (SPIHT) image coder named VSPIHT.

A novel framework for rate-distortion (RD) analysis is developed. Based on this framework, an optimum bit allocation scheme and an accurate rate control algorithm are proposed for real-time video coding with H.263+ (see Cote, G. et al., IEEE Trans. on Circuits and Systems for Video Technology, vol.8, p.849-66, 1998). With the proposed algorithm, the picture quality is significantly improved. The output bit rate of the video encoder is controlled robustly and accurately according to the network condition.

This paper presents a new method for equalizing colors of objects in two images of the same scene taken in different illumination conditions. The method outlined compensates for differences in colors by separately equalizing their achromatic and chromatic components. The equalization of the 1-D achromatic channel is carried out with a standard technique for gray-level images whereas the equalization of the 2-D chromatic channel is considered as a problem of image warping. The experiments reported show the effectiveness of our method.

This paper presents a new technique based on anisotropic diffusion for segmenting color images. This operation is accomplished through two independent anisotropic diffusion processes: one involving only the chromatic information, conveniently embedded in a complex function, and the other affecting the lightness information. The results of the two diffusions are separately segmented and their combination allows the color image to be eventually partitioned. We report on some experimental results verifying the effectiveness of such a technique. 1.

This paper presents a new algorithm for color contrast enhancement which adopts the xy chromaticity diagram and consists of two steps. All the "chromatic" colors are first maximally saturated within a certain gamut; the opportune desaturation operation which follows is based on the center of gravity law for color mixture. This prevents the introduction of unnatural colors and, in combination with a suitable manipulation of the brightness value, turns out to increase the image sharpness and to provide more appealing results Our technique can also be applied to re-rendition a color image since it can easily simulate the change of the illuminant(s) of the scene portrayed in the image, this could find useful applications in image and video editing. Some examples of the performance of the algorithm are reported and discussed.

By introducing the new concepts of characteristic rate curves and rate curve decomposition, a generic source-modeling framework is developed for transform coding of videos. Based on this framework, the rate-quantization (R-Q) and distortion-quantization (D-Q) functions (collectively called R-D functions in this work) of the video encoder can be accurately estimated with very low computational complexity before quantization and coding. With the accurate estimation of the R-Q function, a frame-level rate control algorithm is proposed for DCT video coding. The proposed algorithm outperforms the TMN8 rate control algorithm by providing more accurate and robust rate regulation and better picture quality. Based on the estimated R-D functions, an encoder-based rate-shape-smoothing algorithm is proposed. With this smoothing algorithm, the output bit stream of the encoder has both a smoothed rate shape and a consistent picture quality, which are highly desirable in practical video coding and transmission.

In our previous work, we have developed a rate-distortion (R-D) modeling framework for H.263 video coding by introducing the new concepts of characteristic rate curves and rate curve decomposition. In this paper, we further show it is a unified R-D analysis framework for all typical image/video transform coding systems, such as embedded zero-tree wavelet (EZW), set partitioning in hierarchical trees (SPIHT) and JPEG image coding; MPEG-2, H.263, and MPEG-4 video coding. Based on this framework, a unified R-D estimation and control algorithm is proposed for all typical transform coding systems. We have also provided a theoretical justification for the unique properties of the characteristic rate curves. A linear rate regulation scheme is designed to further improve the estimation accuracy and robustness, as well as to reduce the computational complexity of the R-D estimation algorithm. Our extensive experimental results show that with the proposed algorithm, we can accurately estimate the R-D functions and robustly control the output bit rate or picture quality of the image/video encoder.

This paper presents the quaternion color difference edge detector, a new approach to detection of edges in color images. Based on a new type of convolution, the color difference subspace and the proposed edge detector are expressed analytically by using the algebra of the quaternion. The proposed color image edge detector generates edges only where sharp changes of color occur in the original image. The experimental results have verified the improved performance of the new edge detector compared to some well known methods.

Texture description is important for image retrieval from various large image databases. A method for representing texture information in images utilizing dual tree complex wavelet transform (DT-CWT) is introduced. Approximate shift invariance, good directional selectivity and computational efficiency properties of DT-CWT are effective in describing texture patterns. The perfect reconstruction property of DT-CWT enables us to store the image data using DT-CWT coefficients. Experiments are performed with Brodatz (1966) texture database and nature images that have significant amount of texture information to investigate the efficiency of our texture description algorithm.

In wavelet image compression, all information loss occurs during quantization. Based on the property of bi-orthogonal wavelets, optimal 2-D quantization error feedback filters are used to reduce the reconstruction error. With very low complexity with regard to computation and implementation, the error feedback system improves the PSNR of the reconstructed image by about 0.25 dB. In addition, due to its similar structure to the dithered quantizer, it also improves the subjective quality of the reconstructed image by reducing the contouring and ranging effects.

A coding algorithm of low addressing and implementation complexity is proposed. It is based on partitioning uniformly quantized wavelet coefficients into multiscale blocks with each block classified as either an all-zero block or a non-zero block. The non-zero blocks are coded by a new method called zero-mapping whose outputs are further compressed by a first-order arithmetic coder. The performance of the proposed coding algorithm compares favorably with that of some well-known coding algorithms, particularly for images with considerable high frequency components.

This paper presents a new approach to color filtering which operates on the representation of an image in the xyY color space. The filtering scheme, aided by the color mixing rule which applies to the 2D chromatic subspace spanned by the x and y coordinates, is shown to preserve the convexity of the chromatic information. Some examples of lowpass filtering with the new technique are reported.

The signal-dependent rank order mean (SD-ROM) filter is effective at removing high levels of impulse noise from 2-D scalar-valued signals. Excellent results have been presented for both a two-state and a multi-state version of the filter. However, implementation of the two-state SD-ROM filter requires the selection of a set of threshold values. We propose a method for choosing the thresholds based on a statistical characterization of an input image. The method approximates the histogram of an image with a weighted sum of Gaussian distributions. Using the statistical model and the input distributions, the likelihood of correctly identifying impulses is estimated as a function of the thresholds. By maximizing the likelihood of correct detection, optimal thresholds are predicted. The performance of the algorithm using the predicted thresholds is compared to the optimal performance found using a brute-force search.

We propose a simple but efficient wavelet image compression algorithm. The proposed coding scheme employs the multi-level dyadic wavelet decomposition, linear quantization with a proper dead zone, 1-D addressing complexity by raster scanning within subbands, variable length block coding, small alphabet representation of 1-D integer sequences, and adaptive arithmetic entropy coding. Despite the simplicity of the proposed coding scheme, the rate-distortion performance of the proposed image compression algorithm is competitive with the best image coders in the literature.

A vector enhancement of Said and Pearlman's set partitioning in hierarchical trees (SPIHT) methodology, named VSPIHT, has been proposed for embedded wavelet image compression. A major advantage of vector-based embedded coding with fixed length VQs over scalar embedded coding is its superior robustness to noise. We show that vector set partitioning can effectively alter the balance of bits in the bit steam so that significantly fewer critical bits carrying significant information are transmitted, thereby improving inherent noise resilience. For low noise channels, the critical bits are protected, while the degradation in reconstruction quality caused by errors in noncritical quantization information, can be reduced by appropriate VQ indexing, or designing channel optimized VQs for the successive refinement systems. For very noisy channels, unequal error protection to the critical and noncritical bits with either block codes or convolution codes are used. Additionally, the error protection for the critical bits is changed from pass to pass. A buffering mechanism is used to produce an unequally protected bit stream without sacrificing the embedding property. Extensive simulation results are presented for noisy channels, including bursty channels.

This paper introduces the concept of warped discrete cosine transform (WDCT) and an image compression algorithm based on the WDCT. The proposed WDCT is a cascade connection of a conventional DCT and all-pass filters whose parameters can be adjusted to provide frequency warping. Because only the first-order all-pass filters are considered, the WDCT can be implemented by a Laguerre network connected with the DCT. For the more efficient software implementation, we propose truncated and approximated FIR filter banks which can be used instead of the Laguerre network. As a result, the input-output relationship of the WDCT can be represented by a single matrix-vector multiplication, like the DCT. In the proposed image-compression scheme, the frequency response of the all-pass filter is controlled by a fixed set of parameters from which a specified warping parameter is used for a specified frequency range. Also, for each parameter, the corresponding WDCT matrices are computed a priori. For each image block, the best parameter is chosen from the set and the index is sent to the decoder as side information along with the result of corresponding WDCT matrix computation. At the decoder, an inverse WDCT is performed to reconstruct the image. The WDCT based compression outperforms the DCT based compression, for high bit rate applications and for images with high-frequency components. It results in 1.1-3.1-dB PSNR gain over conventional DCT at 1.5 bpp for natural images, and provides more gain for compound images with texts.

Digital data hiding is a technology being developed for multimedia services, where significant amounts of secure data is invisibly hidden inside a host data source by the owner, for retrieval only by those authorized. The hidden data should be recoverable even after the host has undergone standard transformations, such as compression. In this paper, we present a source and channel coding framework for data hiding, allowing any tradeoff between the visibility of distortions introduced, the amount of data embedded, and the degree of robustness to noise. The secure data is source coded by vector quantization, and the indices obtained in the process are embedded in the host video using orthogonal transform domain vector perturbations. Transform coefficients of the host are grouped into vectors and perturbed using noise-resilient channel codes derived from multidimensional lattices. The perturbations are constrained by a maximum allowable mean-squared error that can be introduced in the host. Channel-optimized VQ can be used for increased robustness to noise. The generic approach is readily adapted to make retrieval possible for applications where the original host is not available to the retriever. The secure data in our implementations are low spatial and temporal resolution video, and sampled speech, while the host data is QCIF video. The host video with the embedded data is H.263 compressed, before attempting retrieval of the hidden video and speech from the reconstructed video. The quality of the extracted video and speech is shown for varying compression ratios of the host video.

A vector enhancement of Said and Pearlman's (1996) set partitioning in hierarchical trees (SPIHT) methodology, named VSPIHT, has recently been proposed for embedded wavelet image compression. While the VSPIHT algorithm works better than scalar SPIHT for most images, a common vector dimension to use for coding an entire image may not be optimal. Since statistics vary widely within an image, a greater efficiency can be achieved if different vector dimensions are used for coding the wavelet coefficients from different portions of the image. We present a generalized methodology for developing a variable dimensional set partitioning coder, where different parts of an image may be coded in different vectoring modes, with different scale factors, and up to different number of passes. A Lagrangian rate-distortion criterion is used to make the optimum coding choices. Coding passes are made jointly for the vectoring modes to produce an embedded bitstream.

This paper introduces the concept of warped discrete cosine transform (WDCT) and an image compression algorithm based on the WDCT. The proposed WDCT is a cascade connection of a conventional DCT and all-pass filters whose parameters can be adjusted to provide frequency warping. In the proposed image compression scheme, the frequency response of the all-pass filter is controlled by a set of parameters with each parameter for a specified frequency range. For each image block, the best parameter is chosen from the set and is sent to the decoder as a side information along with the result of corresponding WDCT coefficients. It is shown that the WDCT can be implemented by a single matrix computation like the DCT. The proposed algorithm outperforms the DCT based compression, for high bit rate applications and for images with high frequency components.

This paper presents an algorithm for unsupervised segmentation of color images. The main idea behind it is the use of the low-frequency content of images which allows for smoothing of segments and sharpening of histograms of color attributes. Our algorithm handles images in a palettized format and operates in the feature space constituted by the cylindrical representation of the L*u*/spl nu/* color space. Within such space, it finds representative colors by determining first the main hue families, through histogram thresholding, and then the main clusters on planes at constant hue, by means of k-means clustering. Two examples of the practical performance of the algorithm are reported and discussed.

Most natural images are well modeled as smoothed areas segmented by edges. The smooth areas can be well represented by a wavelet transform with high regularity and with fewer coefficients which requires high-pass filters with some vanishing moments. However for the regions around edges, short highpass filters are preferable. In one recently proposed approach, this problem was solved by switching filter banks using longer filters for smoothed areas of the images and shorter filters for areas with edges. This approach was applied to lossy image coding resulting in a reduction of ringing artifacts. As edges were predicted using neighboring pixels the nonlinear transforms made the decorrelation more flexible. In this paper we propose a time-varying filterbank and apply it to lossless image coding. In this scheme, we estimate the standard deviation of the neighboring pixels of the current pixel by solving the maximum likelihood problem. The filterbank is switched between three filter banks, depending on the estimated standard deviation.

The set partitioning in hierarchical trees (SPIHT) approach for still image compression proposed by Said and Pearlman (see IEEE Transactions on Circuits and Systems for Video Technology, vol.6, no.3, 1996) is one of the most efficient embedded gray image compression schemes to date. The algorithm relies on a very efficient scanning cum bit-allocation scheme for quantizing the coefficients obtained by a wavelet decomposition of an image. We adopt this scheme to scan vectors of wavelet coefficients, and use successive refinement VQ techniques with staggered bit-allocation to quantize several wavelet coefficients at once. The new scheme is named VSPIHT (vector SPIHT). We present some coding results comparing VSPIHT to the scalar counterpart in the mean-squared-error sense. The method readily generalizes to color images and video where the vector-based approach makes more sense. We present the coding results on intra frames of QCIF sequences as compared against H.263.

A noise reduction algorithm for signals corrupted by additive unknown L/sub 2/ white noise is proposed using an H/sup /spl infin// filtering framework. The proposed algorithm consists of two steps: a signal enhancement step and a parameter estimation step, which are iterated at each instant. To weaken the dependence between the signal enhancement step and the parameter estimation step, a total least squares estimation step for the dynamical model parameters needed in the H/sup /spl infin// filtering is introduced. The effectiveness of the proposed algorithm under low signal-to-noise ratio environments is demonstrated by simulation.

Digital data hiding is a technology being developed for multimedia services, where non-trivial amounts of signature data is invisibly hidden inside a host data source by the owner before the latter is freely distributed. Only those authorized can recover the hidden data from the host, even after the latter has undergone standard transformations such as compression. We adopt a quantitative source and channel coding approach to hiding large amounts of compressible signature data inside the raw host. The signature data is source coded by vector quantization, and the indices are embedded in the host by perturbing it using orthogonal transform domain vector perturbations. The transform coefficients of the parent data are grouped into vectors, and the vectors are perturbed using noise-resilient channel codes derived from multidimensional lattices. The perturbations are constrained by a maximum allowable mean-squared error that can be introduced in the host. The generic approach is readily adapted to make retrieval possible even for applications where the original host is not available to the retriever. This scheme is applied to hiding speech in video. The host video is wavelet transformed frame by frame, and vectors of coefficients are perturbed using lattice channel codes to represent hidden vector quantized speech. The embedded video is subjected to H.263 compression before retrieving the hidden speech from it. The retrieved speech is intelligible even with large compression ratios of the host video.

While lattice vector quantization (LVQ) can solve the complexity problem of LBG based vector quantizers, and also yield very general codebooks, a single stage lattice VQ, when applied to high variance vectors result in very large and unwieldy indices, making it unsuitable for applications requiring successive refinement. The goal of this work is to develop a unified framework for progressive uniform quantization of vectors, without having to sacrifice the mean-squared-error advantage of lattice quantization. A successive refinement uniform vector quantization paradigm is developed, where the codebooks in successive stages are all lattice codebooks, each in the shape of the Voronoi region of the lattice at the previous stage. The Voronoi shaped lattice codebook at each stage is called Voronoi lattice VQ (VLVQ). Measures of efficiency of successive refinement are developed. The developed methodology is applied to successively refine vectors of wavelet coefficients in the vector set-partitioning (VSPIHT) framework to obtain an embedded bitstream. The results are compared against the previous successive approximation wavelet vector quantization (SA-W-VQ) results of Sampson, da Silva, and Ghanbari (see IEEE Trans. Image Processing, vol.5, no.2, p.299-310, 1996) for image coding.

In a great number of fields of computer vision image segmentation plays an essential role as a preliminary step towards further and higher levels of image processing. An original algorithm for unsupervised segmentation of color images is here presented; it resorts to a palletized representation of images, it uses the low spatial frequency content of color which is represented in the CIELUV space and in this space it builds and thresholds hue and chroma histograms finding out the color clusters which allow the image to be segmented. Evidence of the algorithm's effectiveness is reported.

A vector extension of the set partitioning in hierarchical trees (SPIHT) algorithm, named vector-SPIHT (VSPIHT), using trained classified successive refinement VQ, has recently been proposed. In this work, vector set-partitioning is applied to multispectral image compression, in particular to 24-bit color images. Since the individual spectral components are sufficiently correlated, VSPIHT can effectively exploit both the inter-component redundancy as well as the spatial redundancy within each subband of each component, to yield performance superior to separate scalar SPIHT coding of each component. Adaptive arithmetic coding of the first stage VQ index for each class, as well as the significance information, further improves the performance. Coding results demonstrate that the vector-based approach for color images significantly outperforms the scalar counterpart in the mean-squared-error sense.

Three specific programs are suggested to modify the electrical engineering curriculum to keep up with the dramatic technological developments of recent years. One of the programs is a five-year combined BS/MS program which permits the student to specialize in more than one field. The second proposal is to restructure the BS program into a multi-track program. The third one is an internship-in-industry program to provide the student with a meaningful and valuable real-world design experience before graduation.

Summary form only given, as follows. Polyphase decomposition of a sequence was advanced to develop computationally efficient interpolators and decimators, and has also been used to design computationally efficient quadrature-mirror filter banks. The polyphase decomposition represents a sequence into a set of sub-sequences, called polyphase components. However, the polyphase components do not exhibit any spectral separation. In this presentation, we first review the concept of structural subband decomposition, generalization of the polyphase decomposition, which decomposes a sequence into a set of sub-sequences with some spectral separation that can be exploited advantageously in many digital signal processing applications. We then outline some of the applications of the structural subband decomposition, such as efficient design and implementation of FIR digital filters, development of computationally efficient decimators and interpolators, subband adaptive filtering, and fast computation of discrete transforms.

We propose a new class of mapping-based nonlinear quadratic Volterra filters for image enhancement. The input signal is mapped prior to filtering by a memoryless one-to-one nonlinear mapping function. The mapping function can be described by any arbitrary function and implemented by a simple look-up table. If necessary, an inverse mapping function is applied after filtering. Using this general approach, the quadratic Volterra filter output can be adjusted to a desired response. Some results are presented where a high-pass quadratic Volterra filter is used to enhance an image by unsharp masking.

Because of different television standards, format conversion is necessary to interchange video programs globally. To this end, temporal interpolation is required for conversion between formats with different frame rate. Adaptive interpolation based on motion estimation offers movement-oriented filtering and provides significant improvement over other methods. However, algorithms proposed so far do not offer a sufficient conversion quality when the motion in the scene is critical. To overcome this problem, a new algorithm for frame rate up-conversion considering multiple motion is developed. At first, a set of candidate vectors for the true movements are detected by block processing and then the appropriate vectors are assigned pixel-wise. Finally, the missing frames are interpolated using these vectors. The proposed method is evaluated by computer simulation and simulation results are included.

The low bitrate video coding standard H.263 allows four modes of coding, and 31 quantization parameters for each macroblock in a sequence. A new quantization parameter can be set at the beginning of each group of blocks (GOB), and then adapted from macroblock to macroblock within the GOB in a constrained manner. In this work, for every GOB in a frame, an m-best search scheme is employed through a trellis to find the best modes and the best quantizer step changes, in a rate-distortion sense, for both when the starting quantization parameter is predetermined, and when it is to be selected optimally as well. Thus the algorithm performs the most generic kind of optimization at the macroblock level for the P-frames of H.263. It is demonstrated that a relatively low search depth is sufficient to produce coding results superior to established standard-compatible coders.

Image decomposition based on the discrete wavelet transform (DWT) has been proposed for efficient storage and progressive transmission of images for visual browsing in digital image libraries. Although the compression aspects of the DWT have been carefully researched, reconstruction errors due to corrupted wavelet coefficients have received less attention. In this paper we consider the problem of bit errors affecting uniformly quantized wavelet coefficients. The proposed method, which is based on a local image model, simultaneously detects and masks corrupted wavelet coefficients.

In this paper, a contrast pyramid based image coding method is described in which a simple nonlinear difference operation is introduced to generate residual information between two contiguous level images. The representation of the residual information can be considered as a local contrast measure. As the difference image in established pyramid coding techniques, the contrast image has low variance, and data compression is achieved by quantizing the contrast image. Based on Weber's law and spatial masking of the human visual system, further data compression can be attained by selecting only perceptually significant information from the contrast image and coding it efficiently.

Systems containing both analog and digital functions have been investigated with the purpose of realizing mixed-signal integrated circuits with higher levels of functionality and integration. In most cases, such mixed-signal systems are inherently multirate because of the different sampling rates employed at various stages of the system. The multirate concepts have been used for traditional applications, such as subband coding and narrowband filter design. Some unconventional applications of multirate signal processing are also emerging, both for converting between analog samples and digital words, and for realizing processing functions in an easier and more economical way than would be possible using purely digital or analog techniques. This paper reviews fundamental multirate concepts, discusses some developments in this area of integrated multirate analog-digital systems, and outlines some possible future directions for research and application.

An adaptive vector quantization (VQ) scheme with codebook transmission is derived for the variable-rate source coding of image data using an entropy-constrained Lagrangian framework. Starting from an arbitrary initial codebook C(I) available to both the encoder and decoder, the proposed algorithm iteratively generates an improved operational codebook C(0) that is well adapted to the statistics of a particular image or subimage. Unlike other approaches, the rate-distortion trade-offs associated with the transmission of updated code vectors to the decoder are explicitly considered in the design. In all cases, the algorithm guarantees that the operational codebook C(0) will have rate-distortion performance (including all side-information) better than or equal to that of any initial codebook C(I). When coding the Barbara image, improvement at all rates is demonstrated with observed gains of up to 3 dB in peak signal-to-noise ratio (PSNR). Whereas in general the algorithm is multipass in nature, encoding complexity can be mitigated without an exorbitant rate-distortion penalty by restricting the total number of iterations. Experiments are provided that demonstrate substantial rate-distortion improvement can be achieved with just a single pass of the algorithm.

We consider the problem of implementing perfect reconstruction modulated polyphase filter banks having infinite impulse response (IIR) subfilters in systems that must process infinite length 1-D inputs. This task is complicated by the fact that the synthesis bank needed to ensure perfect reconstruction in such a system generally has noncausal or reverse-time filter sections. To overcome this limitation, we develop a number of unique buffering schemes that make possible the implementation of such reverse-time filters with infinite length signals. For the important special case when the polyphase subfilters are allpass, we also present a method that allows for very efficient implementation of tree-structured filter banks and wavelet transforms. We then describe a wideband coding algorithm based largely on work done by Lokhoff (1991) and Johnston (1980, 1988). Using this algorithm, we compare the performance of IIR filter banks with that of more conventional pseudo-QMF and tree-structured QMF banks. The results of these comparisons indicate that one of our filter banks-a tree-structured allpass bank-achieves slightly better performance than equivalent FIR banks in terms of rate and distortion (both objectively and subjectively measured) while requiring lower computational complexity.

This paper re-examines modulated polyphase filter banks which use reverse-time subfilters to achieve perfect reconstruction and studies their performance for image coding when used to form a wavelet decomposition. To code the wavelet coefficients, we use the embedded zerotree wavelet (EZW) algorithm developed by Shapiro (1993) which is reasonably simple and yet achieves very good rate-distortion performance. The problem of eliminating filter transients is thoroughly studied and optimal results are derived in both the absence and presence of subband coefficient quantization. Using this analysis as a starting point, we develop a new method of coding the filter states (required to eliminate edge transients) for transmission to the receiver which efficiently exploits interscale redundancy and is easily incorporated into the zerotree algorithm. Comparing this direct transmission method to circular convolution, we find that it achieves superior rate-distortion performance in a wide range of cases. Coding comparisons between two infinite impulse response (IIR) wavelets and a number of biorthogonal wavelets are presented. These comparisons indicate that the performance of the polyphase allpass wavelet is comparable to that of the best finite impulse response (FIR) biorthogonal wavelets with considerably reduced computational complexity.

The discrete cosine transform (DCT) is well known for its highly efficient coding performance and is widely used in many image compression applications. However, in low bit rate coding, it produces undesirable block artifacts that are visually not pleasing. In addition, in many practical applications, faster computation and easier VLSI implementation of DCT coefficients are also important issues. The removal of the block artifacts and faster DCT computation are therefore of practical interest. In this paper, we investigate a modified DCT computation scheme, to be called the subband DCT (SB-DCT), that provides a simple, efficient solution to the reduction of the block artifacts while achieving faster computation. We have applied the new approach for the low bit rate coding and decoding of images. Simulation results on real images have verified the improved performance obtained using the proposed method over the standard JPEG method.

A method for rate-distortion optimal variable rate mean-gain-shape vector quantization (MGSVQ) is presented with application to image compression. Conditions are derived within an entropy-constrained product code framework that result in an optimal bit allocation between mean, gain, and shape vectors at all rates. An extension to MGSVQ called hierarchical mean-gain-shape vector quantization (HMGSVQ) is similarly introduced. By considering the statistical dependence between adjacent means, this method is able to provide an improvement in the rate-distortion performance over traditional MGSVQ, especially at low bit rates. Simulation results are provided to demonstrate the rate-distortion performance of MGSVQ and HMGSVQ for image data.

This paper addresses the problem of encoder optimization in a macroblock-based multimode video compression system. An efficient solution is proposed in which, for a given image region, the optimum combination of macroblock modes and the associated mode parameters are jointly selected so as to minimize the overall distortion for a given bit-rate budget. Conditions for optimizing the encoder operation are derived within a rate-constrained product code framework using a Lagrangian formulation. The instantaneous rate of the encoder is controlled by a single Lagrange multiplier that makes the method amenable to mobile wireless networks with time-varying capacity. When rate and distortion dependencies are introduced between adjacent blocks (as is the case when the motion vectors are differentially encoded and/or overlapped block motion compensation is employed), the ensuing encoder complexity is surmounted using dynamic programming. Due to the generic nature of the algorithm, it can be successfully applied to the problem of encoder control in numerous video coding standards, including H.261, MPEG-1, and MPEG-2. Moreover, the strategy is especially relevant for very low bit rate coding over wireless communication channels where the low dimensionality of the images associated with these bit rates makes real-time implementation very feasible. Accordingly, in this paper, the method is successfully applied to the emerging H.263 video coding standard with excellent results at rates as low as 8.0 Kb per second. Direct comparisons with the H.263 test model, TMN5, demonstrate that gains in peak signal-to-noise ratios (PSNR) are achievable over a wide range of rates.

A new framework for removing impulse noise from images is presented in which the nature of the filtering operation is conditioned on a state variable defined as the output of a classifier that operates on the differences between the input pixel and the remaining rank-ordered pixels in a sliding window. As part of this framework, several algorithms are examined, each of which is applicable to fixed and random-valued impulse noise models. First, a simple two-state approach is described in which the algorithm switches between the output of an identity filter and a rank-ordered mean (ROM) filter. The technique achieves an excellent tradeoff between noise suppression and detail preservation with little increase in computational complexity over the simple median filter. For a small additional cost in memory, this simple strategy is easily generalized into a multistate approach using weighted combinations of the identity and ROM filter in which the weighting coefficients can be optimized using image training data. Extensive simulations indicate that these methods perform significantly better in terms of noise suppression and detail preservation than a number of existing nonlinear techniques with as much as 40% impulse noise corruption. Moreover, the method can effectively restore images corrupted with Gaussian noise and mixed Gaussian and impulse noise. Finally, the method is shown to be extremely robust with respect to the training data and the percentage of impulse noise.

An inherent problem in most image enhancement schemes is the amplification of noise, which, due to Weber's law, is mostly visible in the darker portions of an image. Using a special class of quadratic Volterra filters, we can adapt the enhancement process in a computationally efficient way to the local image brightness because these filters are approximately equivalent to the product of a local mean estimator and a highpass filter. We analyze and derive this subclass of quadratic Volterra filters by investigating the 1-D case first, and then we generalize the results to two dimensions. An important property of these filters is that they map sinusoidal inputs to constant outputs, which allows us to develop a new filter characterization that is more intuitive for our application than the 4-D frequency response. This description finally leads to a novel least-squares design methodology. Image enhancement results using our Volterra filters are superior to those obtained with standard linear filters, which we demonstrate both quantitatively and qualitatively.

Proposes an efficient nonlinear algorithm to suppress impulse noise from highly corrupted images while preserving details and features. The method is applicable to all impulse noise models, including fixed valued (equal height or salt and pepper) impulses and random valued (unequal height) impulses, covering the whole dynamic range. The algorithm is based on a detection-estimation strategy. If a signal sample is detected as a corrupted sample, it is replaced with an estimation of the true value, based on neighborhood information. Otherwise it is kept unchanged. The technique achieves excellent tradeoff between the suppression of noise, and preserving the details and edges without undue increase in computational complexity. Extensive simulation tests indicate that the method performs better than other existing algorithms, including the well known median filters. Illustrative examples included in the paper verify the capability of the proposed approach.

The optimal design of quadtree-based vector quantizers is addressed. Until now, work in this area has focused on optimizing the quadtree structure for a given set of leaf quantizers with little attention spent on the design of the quantizers themselves. In cases where the leaf quantizers were considered, codebooks were optimized without regard to the ultimate quadtree segmentation. However, it is not sufficient to consider each problem independently, as separate optimization leads to an overall suboptimal solution. Rather, joint design of the quadtree structure and the leaf codebooks must be considered for overall optimality. The method we suggest is a "quadtree" constrained version of the entropy-constrained vector quantization design method. To this end, a centroid condition for the leaf codebooks is derived that represents a necessary optimality condition for variable-rate quadtree coding. This condition, when iterated with the optimal quadtree segmentation strategy of Sullivan and Baker (see IEEE Trans. on Image Processing, vol.3, p.327-331, May 1994) results in a monotonically descending rate-distortion cost function, and consequently, an (at least locally) optimal quadtree solution.

A method for efficiently selecting the operating modes within a block-based multi-mode video compression system is described. For a given image region, the optimum combination of modes is selected so as to minimize the overall distortion for a given bit-rate budget. Necessary conditions for optimizing the encoder operation are derived within a rate-constrained product code framework. When rate and distortion dependencies exist between adjacent blocks, the ensuing encoder complexity is surmounted using a dynamic programming strategy based on the Viterbi algorithm so as to achieve the optimum selection of macroblock modes. Results are provided for the emerging H.263 video coding standard.

An algorithm based on the subband nonuniform discrete Fourier transform (SB-NDFT) is proposed for decoding dual-tone multi-frequency (DTMF) signals. To decode a DTMF signal, its energy at the eight DTMF frequencies must be determined by evaluating samples of the NDFT at these frequencies. In the proposed SB-NDFT algorithm, these NDFT samples are computed by decomposing the input signal into two subbands. Since DTMF signals occupy the low-frequency part of the telephone bandwidth, the higher subband can be discarded for a fast, approximate computation. A performance comparison between algorithms based on the NDFT, SB-NDFT, DFT, and SB-DFT shows that the SB-NDFT requires the lowest number of computations to attain a specified level of performance.

A new framework for removing impulse noise from images is presented in which the nature of the filtering operation is conditioned on a state variable. As part of this state-based framework, several sliding-window algorithms are examined, each of which is applicable to fixed and random-valued impulse noise models. First, a simple two-state approach is described in which the current state is computed according to the output of a simple classifier that operates on the differences between the input pixel and the remaining rank-ordered pixels in the current window. Based on the value of the state variable, the algorithm switches between the output of an identity filter and an order-statistic (OS) filter. For a small additional cost in memory, this simple strategy is easily generalized into a multi-state approach using weighted combinations of the identity and OS filters in which the weighting coefficients can be optimized using image training data. Extensive simulations indicate that these methods perform significantly better in terms of noise suppression and detail preservation than a number of existing nonlinear techniques with as much as thirty percent impulse noise. Finally, the method is shown to be extremely robust with respect to the training data and the percentage of impulse noise.

Image registration is concerned with the establishment of correspondence between images of the same scene. One challenging problem in this area is the registration of multispectral/multisensor images. In general, such images have different gray level characteristics, and simple techniques such as those based on area correlations cannot be applied directly. On the other hand, contours representing region boundaries are preserved in most cases. The authors present two contour-based methods which use region boundaries and other strong edges as matching primitives. The first contour matching algorithm is based on the chain-code correlation and other shape similarity criteria such as invariant moments. Closed contours and the salient segments along the open contours are matched separately. This method works well for image pairs in which the contour information is well preserved, such as the optical images from Landsat and Spot satellites. For the registration of the optical images with synthetic aperture radar (SAR) images, the authors propose an elastic contour matching scheme based on the active contour model. Using the contours from the optical image as the initial condition, accurate contour locations in the SAR image are obtained by applying the active contour model. Both contour matching methods are automatic and computationally quite efficient. Experimental results with various kinds of image data have verified the robustness of the algorithms, which have outperformed manual registration in terms of root mean square error at the control points.

A multipath channel in television broadcasting can result in overlaid images (ghosts) or distorted noisy images on the display and is a major problem to be overcome. We propose a method to equalize the multipath distortion for the case of digital transmission and nonminimum phase channels. The method employs noncausal allpass recursive filters operating in reversed time followed by a decision feedback equalizer (DFE). It does not require the computation of zeros of the channel impulse response, and the channel noise level is not enhanced. The equalized impulse response is such that, in most cases, the first nonnegligible sample has the largest magnitude, as appropriate for DFE decoders. Computer simulation results verifying the proposed approach are included.>

Proposes a modification to the classic time-frequency permutation method of signal scrambling which reduces its complexity and memory requirements without decreasing its performance. This new approach is applicable to any filter bank or transform and requires only that the decomposition in question be implemented in a polyphase form. To minimize the computational complexity, modulated polyphase filter banks like the cosine-modulated and allpass filter banks can be selected. Using a two dimensional extension to the basic algorithm, the authors consider the problem of image scrambling and include simulation results.>

In the image fusion scheme presented in this paper, the wavelet transforms of the input images are appropriately combined, and the new image is obtained by taking the inverse wavelet transform of the fused wavelet coefficients. An area-based maximum selection rule and a consistency verification step are used for feature selection. A performance measure using specially generated test images is also suggested.>

An adaptive entropy-constrained codebook design algorithm for vector quantization (VQ) of image data is proposed. The algorithm iteratively updates the code vectors of an initial general-purpose codebook C/sub T/ in order to generate an improved operational codebook C/sub O/ that is well-adapted to the statistics of a particular image or sub-image. Unlike other approaches, the rate-distortion trade-offs associated with transmitting updated code vectors to the decoder are explicitly considered in the design. An optimal trade-off is made possible by the entropy-constrained framework. For any image, the algorithm guarantees that the operational codebook C/sub O/ will have rate-distortion performance (including all side-information) better than or equal to that of any initial codebook C/sub T/. When coding the "Barbara" image, improvement at all rates is demonstrated with gains of up to 3 dB in PSNR observed.>

While product code VQ is an effective paradigm for reducing the encoding search and memory requirements of vector quantization, a significant limitation of this approach is the heuristic nature of bit allocation among the product code features. We propose an optimal bit allocation strategy for PCVQ through the explicit incorporation of an entropy constraint within the product code framework. Unrestricted entropy-constrained PCVQs require joint entropy codes over all features and concomitant encoding and memory storage complexity. To retain manageable complexity, we propose "product-based" entropy code structures, including independent and conditional feature entropy codes. We also propose an iterative, locally optimal encoding strategy to improve performance over greedy encoding at a small cost in complexity. This approach is applicable to a large class of product code schemes, allowing joint entropy coding of feature indices without exhaustive encoding. Simulations demonstrate performance gains for image coding based on the mean-gain-shape product code structure.>

Differential pulse-code modulation (DPCM) has found many applications in both intraframe and interframe coding of images. To improve its performance, several adaptive techniques have been introduced, but they make the resulting DPCM systems very complicated. In this work, we introduce a nonlinear scheme of predictive coding to exploiting spatial redundancy and amplitude redundancy of images based on the characteristics of the human visual system. The proposed scheme consists of a novel nonlinear algorithm to generate new information and a new compandor model of uniform quantization.>

Images are often corrupted by impulse noise from a noisy sensor or channel transmission errors. The goal of impulse noise removal is to suppress the noise while preserving the edges and the details. To this end, nonlinear techniques have been found to provide more satisfactory results in comparison to linear methods. The two often used nonlinear methods are the median filter and the outlier method. In median filtering the central pixel inside a window is replaced by the median value of all pixels in the window. However, median filtering not only removes impulse noise but also introduces distortion, in particular, for highly corrupted images. The outlier method is based on a detection-estimation strategy in which the impulse noise is detected first and then an average of all pixel values inside a window centered at the defected corrupted pixel is used as an estimate of its true value. This approach is also not effective for highly corrupted images. Recently, we proposed an efficient method to remove impulse noise from a highly corrupted image also based on a detection-estimation strategy, in which the impulse noise is detected first using a simple quadratic filter, and a selectively chosen local mean is used to estimate the true value of the corrupted pixel. A major limitation of this approach is that often it has to be applied twice to arrive at a satisfactory result. This second run not only increases computational cost but also reduce the quality of the processed image. In this paper, we analyze the limitation of this newly proposed method of impulse noise removal, and then advance a modified version which does not require a second run.>

This paper investigates the use of the generalized structural subband implementation of adaptive FIR filters in high-speed fault tolerant adaptive filtering. The convergence behavior of the proposed fault tolerant adaptive structure, after a coefficient fault has occurred, is analyzed. The problems of identifying the occurrence of a fault and the faulty coefficient are examined. The convergence behavior of the proposed subband structure during a fault occurrence is compared to the behavior of previously reported structures.>

A novel feature extraction technique based on a new class of nonlinear filters is presented for perceptually based, low bit rate image compression. In addition to having remarkable computational efficiency, the filters adaptively extract perceptually relevant edge and texture information with less amplification of noise than conventional linear filters. A two-band nonlinear decomposition based on the filters is constructed so that this feature information can be separated from the image. Separate coding strategies are examined that effectively quantize these features and the more stationary, low frequency residual information. The resulting compression scheme is compared with traditional methods of image compression and is shown to exhibit clear advantages in perceptual reconstruction quality.

We propose a novel method for image interpolation which adapts to the local characteristics of the image in order to facilitate perfectly smooth edges. Features are classified into three categories (constant, oriented, and irregular). For each class we use a different zooming method that interpolates this feature in a visually optimized manner. Furthermore, we employ a nonlinear image enhancement which extracts perceptually important details from the original image and uses these in order to improve the visual impression of the zoomed images. Our results compare favorably to standard lowpass interpolation algorithms like bilinear, diamond- filter, or B-spline interpolation. Edges and details are much sharper and aliasing effects are eliminated. In the frequency domain we can clearly see that our adaptive algorithm not only suppresses the undesired spectral components that are folded down in the upsampling process. It is also capable of replacing them with new estimates, which accounts for the increased image sharpness. One application of this interpolation method is spatial interlaced-to- progressive conversion. Here, it yields again more pleasing images than comparable algorithms.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

An image representation scheme using a set of block pattern models (BPMs) consisting of three categories (constant, oriented, and irregular) is introduced. Algorithms for model classification, model parameter estimation, and image reconstruction from model parameters are presented, and these provide the necessary vehicles for applying the proposed representation scheme to various image processing tasks. The applications of the proposed models in image coding, image zooming, and image smoothing are described. Satisfactory coded images have been obtained at bit rates between 0.5 approximately 0.6 b.p.p. (bits per pixel) with a high-rate realization and between 0.3 approximately 0.5 b.p.p. with a low-rate realization. The high-rate realization has a simple structure suitable for real-time implementation. The methods for image zooming and smoothing are similar, where both adapt the processing for each pixel according to the model of its neighborhood. By using directional filters in oriented regions, edges and lines are rendered sharper in a smoother manner than with conventional linear filtering approaches, which leads to significant improvement in perceived image quality.>

A multiprocessor code generation method for digital signal processing algorithms represented by SFGs (signal flow graphs) is developed. For reducing the number of communication operations as well as distributing the workload evenly among the processors, a multiprocessor scheduling method based on a parallel block processing scheme, which processes multiple blocks of input data concurrently, is employed. The developed method first divides an SFG into graph segments to reduce the dependency time. A segment merging process is followed, which results less number of temporary data storages and data transfers. A multiprocessor code is generated by applying a single processor code generation method to each of these segments. The implementation result for QR-RLS algorithm using the developed method is included.>

An efficient real-time implementation of digital filtering algorithms using a multiprocessor system in a ring network is investigated. This method is based on a parallel block processing approach, where a continuously supplied input data is divided into blocks, and the blocks are processed concurrently by being assigned to each processor in the system. This approach requires only a simple interconnection network and reduces significantly the number of communications among the processors, making the system easily expandable and highly efficient. In addition, various digital signal processing algorithms can be implemented on the same multiprocessor system. The data dependency of the blocks to be processed concurrently brings on dependency problems between the processors. A systematic scheduling method has been developed by using a precedence graph for the analysis of the dependency relation. Methods for solving the dependency problems between the processors are also investigated. Implementation procedures and results for FIR, recursive, and adaptive filtering algorithms are illustrated.>

Two types of very simple two-dimensional nonlinear filters are introduced and applied to image contrast enhancement. The first type is based on a generalization of the Teager's algorithm. A theoretical analysis has shown that this type of nonlinear filter works like a local-mean-weighted highpass filter. Based on this analysis, a second type of nonlinear filter has been developed which works like local-mean-weighted bandpass filter. The proposed image contrast enhancement technique is based on combining the original image with its filtered version obtained using one of the two nonlinear filters. Very high quality enhancement has been achieved for natural images.>

A method for estimating the power spectral density (PSD) of a given input sequence is proposed. The method is derived as a simple extension of the subband decomposition fast Fourier transform algorithm. A simple tree-structured subband decomposition of the input sequence is applied using only additions and subtractions. A minor addition to the algorithm allows at each decomposition stage the computation of an estimate of the autocorrelation coefficients of the respective input sequence. The overall PSD estimate is then obtained by properly combining the outputs of the separate stages. The method is best suited for estimating the frequency band containing most of the signal power and can be used by itself as an estimate and/or as an integral part of data-driven algorithms to compute a limited number of transform points, to initialize transform domain adaptive algorithms.>

An edge detection scheme which exploits both the magnitude and orientation information of a gradient image is presented. A pixel with a large gradient is considered as an edge element only if the samples in its neighborhood have a unique orientation (straight edge) or a few strong directions (mixed edge). By making use of the orientation information, the proposed scheme can effectively distinguish between the edge points defining object boundaries and those constituting texture patterns. It is also insensitive to noise since the detection is based on the orientation assumed by the majority of the pixels in a neighborhood instead of the individual orientation or intensity variation.>

A hybrid motion/pattern adaptive scheme for the conversion of interlaced video sequences to the progressive format is presented. It normally operates in the temporal interpolation model and switches to spatial interpolation when motion is detected. The filter for spatial interpolation is adapted according to the local image pattern. Directional filters are designed for oriented features based on their representation by oriented polynomials. Although the proposed scheme has only been applied to the interpolation of interlaced signals, its principle is applicable to other problems in video signal resolution enhancement.>

A technique is presented for efficient coding of the upper bands in subband coding (SBC) of images. The technique takes advantage of the existing correlation between the subbands and utilizes a local measure of activity in the baseband to predict the amplitude range of the pixels in the upper bands. This permits the design of quantizers better adapted to specific images, thus increasing the coding efficiency as well as enhancing the signal-to-noise ratio (SNR) and the subjective perception. The properties of the proposed technique are not fully investigated, but rather its advantages over standard techniques are demonstrated based on some simple cases.>

The fast approximated discrete transform is proposed as a method for reducing the time necessary to compute the discrete transform of a finite-length sequence. It is based on a subband decomposition and can be viewed as a link between the fast transform methods (like the fast Fourier transform), which compute all points in the transform domain, and the variety of methods to evaluate the discrete transforms at a given set of points. The method uses knowledge about the input signal to obtain an approximation to its transform by discarding the computations in bands that have little or no energy contribution. In a number of practical cases the proposed fast approximation is reasonably accurate, and in all cases the method can be iterated to yield the exact transform, if necessary.>

Blind adaptive equalization for digital data storage using a digital signal processing method is presented. In this method the input signal is first sampled at a fixed frequency at N-times the channel bit rate, and then the sampled signal is equalized adaptively with the desired signal generated by a polyphase waveform estimator. As the equalizer is working at the fixed and low sampling rate of the input sequence, the hardware realization is simple, and there is a reduction of the amount of data, making the evaluation of the write/read properties of the storage systems simple. The method is also applicable to the fully digital signal processing data detection system.>

An algorithm that removes impulse noise in images using a modified dynamic programming method is outlined. The restoration process combines two operations. In the first operation, the pixels corrupted by impulse noise are detected by a dynamic programming based searching strategy. In the second operation, the original gray levels of the noisy pixels are estimated by a linear interpolation or extrapolation approach. A separable process is used to detect the noisy pixels of the images. In order to preserve the details of the images and reduce the computational complexity of conventional dynamic programming, two modifications have been developed. One is called neighborhood searching with an adaptive figure of merit and the other is called overlapping block processing. The actual performance of the proposed technique is compared with that of the commonly used median filter by filtering noise-corrupted images. Some computational considerations are also discussed.>

A novel structure for multirate adaptive filtering with lower computational complexity and improved performance of the adaptive algorithm is introduced. It uses auxiliary subbands and a modified filter bank with decimated subbands. It avoids the aliasing distortions encountered in critically decimated overlapping filter banks as well as the spectral gaps in nonoverlapping filter banks. The authors show that this structure has a lower computational complexity than previously reported structures. Computer simulations are included showing the improvement in performance that can be achieved with the new structure operating as an adaptive line enhancer (ALE) compared with the conventional ALE.>

The authors consider a prototype-based binary image classifier that makes comparisons based on blurred representations of the images. The blurring induces a metric on the space of all images that varies continuously under continuous deformation of the image plane. This blurred representation is suitable for direct implementation of a nearest-neighbor classifier. However, it is still desirable to have a representation which is invariant under certain spatial deformations, such as rotation, translation, and scaling of the image plane. A representation which is invariant under these transformation is produced by transforming an input to a local minimum of its distance from each prototype simultaneously. These minima are found by performing a gradient descent on an appropriate error surface over the transformation parameters. The error functional is the L/sub 2/-norm of the difference between the blurred prototype and the blurred input. The resulting classifier makes more efficient use of prototypes than does the nearest-neighbor classifier.>

A class of linear-phase digital filters is discussed for which the filter coefficients are simple functions of the parameters determining the desired frequency response. In the case of lowpass filters, the 6-dB cutoff frequency is the parameter considered. High-pass, bandpass, bandstop, and notch filters can be obtained with simple transformations from a low-pass prototype. The filters are variable over nearly the whole frequency range from zero to half the sampling frequency. Due to direct control of filter coefficients, the length of the filter does not change when it is made variable.>

A new procedure for checking the stability of 2-D digital filters is proposed. The key part of the test involves construction of related allpass sections of reduced order, stability of which is shown to be equivalent to the stability of the original function. The results are shown to be equivalent to some known stability testing methods in 2-D, but have the advantage of an additional insight gained from the circuit interpretation. Explicit formulas for checking the stability in terms of the filter coefficients are derived for some special cases, and numerical examples are included to clarify the application of the proposed approach.>

A coding scheme which encodes each contiguous block of an image based on its local structure is developed. Three different types of models are constructed to characterize the image patterns occurring most frequently in a small block. The average bit rate is reduced by making use of the special constraint among the pixels in an oriented model, where the intensity variation is along only one direction. Judging from the image quality around edges, the reconstructed images with a bit rate less than 0.68 bit/pixel are perceptually superior to those obtained by the block and truncation coding at a bit rate of 1.64 bits/pixel. The complexity of this algorithm increases linearly with the size of the block and the number of orientations considered, which is much lower than that of the standard vector quantization techniques.>

The authors formulate a block-based least-squares problem in the frequency domain. They then develop computationally efficient block least-squares algorithms that can be realized using the fast Fourier transform. They also present computer simulation results demonstrating the convergence characteristics of the proposed algorithms.>

The properties of digital all-pass filters are reviewed and a broad overview of the diversity of applications in digital filtering is provided. Starting with the definition and basic properties of a scalar all-pass function, a variety of structures satisfying the all-pass property are assembled, with emphasis placed on the concept of structural losslessness. Applications are then outlined in notch filtering, complementary filtering and filter banks, multirate filtering, spectrum and group-delay equalization, and Hilbert transformations. In all cases, the structural losslessness property induces very robust performance in the face of multiplier coefficient quantization. Finally, the state-space manifestations of the all-pass property are explored, and it is shown that many all-pass filter structures are devoid of limit cycle behavior and feature very low roundoff noise gain.>

The simple least mean-square (LMS) algorithm shows slow convergence rate, while the computationally-intensive least squares (LS) algorithm has very fast convergence speed. The LMS algorithm realized in the frequency domain is known to have significantly improved convergence rate with moderate complexity. In this work we study new adaptive algorithms that take advantage of both the LS and frequency-domain techniques. We develop several frequency-domain LS algorithms and investigate their performance characteristics by computer simulation.

This correspondence describes a new algorithm for extracting edges from natural images. Starting from a simple image model, the algorithm poses the problem of edge extraction as a statistical classifier problem. The algorithm is capable of extracting and detecting edges from images even in the presence of noise. A step by step mathematical derivation of the algorithm reveals the flexibility of the algorithm with pertinent parameters that can be varied for the specific need of the user. Finally, the proposed edge operator is compared to the well-known Marr-Hildreth's edge operator.

Provides an overview of the technical articles and features presented in this issue.

The implementation of digital filtering algorithms using pipelined vector processors is investigated. Modeling of vector processors and vectorization methods are explained, and then the performances of several implementation methods are evaluated based on the model. Vector processor implementation of FIR filtering algorithms using the outer product method and the indirect convolution method is evaluated. Recursive and adaptive filtering algorithms, which lead to dependency problems in direct vector processor implementations, are implemented very efficiently using a newly developed vectorization method. The proposed method computes multiple output samples at a time, making the vector length independent of the filter order. Illustrative examples comparing theoretical results with Cray X-MP simulation results are included.

A number of well-known stability-test procedures for continuous-and discrete-time systems are re-examined in a unified manner, leading to well-defined network-theoretic interpretations. The representation and network interpretation are based on the fact that the stability of any linear system (scalar or multivariable) is equivalent to the stability of a related all-pass system, which in turn can always be synthesized as a cascade of (scalar or matrix) two-pair all-pass (lossless) networks. The original system of interest is stable if and only if each all-pass two-pair is stable (and hence "lossless bounded real"). As a result of this interpretation, a number of related issues, such as enumeration of unstable poles, prematured terminations, and singularity situations can all be approached in a unified manner, based only on "two-pair extraction formulas." In addition, the network interpretation also leads to direct test procedures for testing relative stability, and the stability of multi-input, multi-output systems.

A new frequency-domain based image edge enhancement technique is described. In the proposed method, the magnitude of the transform of an image is modified using a novel amplitude change function with the phase kept invariant, which is followed by an inverse transform resulting in the crispening of the edge. The new method is somewhat similar to the alpha-rooting method but does not suffer from certain objectionable artifacts associated with the latter, and also exhibits less degradation due to noise. A post-processing of the enhanced image generated using the proposed transform amplitude sharpening method via histogram modification has been found to improve the image quality. Images enhanced with the proposed method are included to illustrate the method.

This paper introduces a new class of uniform digital filter banks based on DFT and recursive Nth-band filters. We consider both even and odd types of channel stacking arrangements. Due to the use of the DFT, the basic filter bank is complex. Real filter banks are obtained by adding the output signals from two symmetrically located complex channels. The filter banks are designed to satisfy the power complementarity and allpass complementarity constraints with high accuracy. Furthermore, nearly alias-free analyzer-synthesizer system can be obtained in the critically sampled case.

Efficient computation method for the recursive digital filtering is studied in the multi-processor environment. The method solves the dependency problem by separate computations of the particular and transient solutions. The throughput of the algorithm increases linearly with the number of processors, making it possible to increase the throughput effectively by using multiple number of processors. The implementations of the algorithm using a vector-processor and a multiprocessor in a ring network are also studied.

It is shown that a wide class of real-coefficient, doubly-complementary IIR transfer-function pairs can be implemented by means of a single complex allpass filter. For a real input sequence, the real part of the output sequence of the complex allpass filter corresponds to one of the transfer functions G(z) (for example, low-pass), whereas the imaginary part of the output sequence corresponds to its "complementary" filter H(z) (for example, highpass). Since the resulting implementation is structurally lossless, G(z) and H(z) have very low passband-sensitivity. Numerical design examples are included to demonstrate the ideas.

The concept of complementary one-dimensional digital filters is extended here to the two-dimensional case. An application of the complementary two-dimensional filters is described and illustrated with the aid of an example.

The class of digital filter pairs satisfying two types of complementary properties simultaneously is reexamined. The pair is required to have complementary square magnitude characteristics with respect to a constant and transfer functions complementary with respect to an allpass function. This filter class, called doubly complementary filters is then extended to have M filters with complex outputs. Basic properties of the filters are discussed. It is shown that all the filters in the bank can be implemented as linear combinations of the same low order allpass filters. The individual filters can have different bandwidths and tolerances. The filter bank can also produce [M/2]+1 real outputs with allpass complementary responses that can be arbitrarily added up to form a variety of allpass complementary filters. The filters have low coefficient sensitivities in their passbands if the allpass sections are implemented with structures that are canonic with respect to the coefficients.

A general framework for the design of an FIR filter based on the cascade of an FIR pre-filter with quantized coefficients followed by an all pole IIR stage is proposed. A simple design method results by designing the pre-filter stage coefficients via a differential coding scheme. The IIR stage is then simply a linear predictor reconstruction stage. The differential coding method eliminates the redundancies of the filter coefficient sequence and makes it possible to quantize the coefficients into a few levels. A linear prediction algorithm is applied to optimize the differential coding method using the statistical characteristics of the given filter. Relatively wideband filters as well as narrowband filters have been sucessfully designed without interpolating the original filters. Overall design procedures and design examples for a variety of filters are included, and the theoretical aspects of this approach are studied.

According to the sampling theorem, a faster sampling rate is required in order to process signals containing high frequency components. The processing rate is restricted by the highest operating speed of devices available. This paper presents the design of N-path parallel processing technique which would overcome the speed limitation of present devices. The transfer function of N-path digital filter is shown to be H(zN), where H(z) is the transfer function of each component filter block. This implies that the overall magnitude response of N-path digital filter is a frequency scaled version of that of component filter. In the proposed paper, a scheme to cancel out the unwanted passbands by cascading several N-path filters is first discussed. Then the design procedure of N-path filter from given specification is illustrated using simple example.

A new type of cascade form structure for digital filtering is proposed, with each building block being a second order section, that satisfies certain passivity properties. This passivity is essentially a "structure-induced" boundedness on the transfer function magnitude, and leads to low passband sensitivity. In addition, the cascade nature ensures low stopband sensitivity, as zeros on the unit circle continue to remain on the unit circle in spite of the quantization. The structure itself is independent of the pole locations and therefore meets a wide range of filtering applications.

In a recent paper [1], it is shown that a fundamental requirement for low passband sensitivity realization of a digital transfer function is that the implementation be structurally passive, or bounded. In this paper, a general procedure for developing low-sensitivity realizations of a transfer function is advanced. The resulting structures are in the form of a cascade connection of basic digital two-pair structures satisfying a "lossless" property in the z-domain. The methods advanced here cover the well-known wave digital filters and the Gray-Markel lattices as special cases. The synthesis procedure is entirely z-domain based, and does not make reference to continuous time networks, unlike the wave digital filters which are designed starting from a continuous time network.

A unified approach to the efficient realization of FIR adaptive digital filters in both the time and frequency domains is presented. It is shown that previously published frequency domain implementations are contained within this unified approach. It is further shown that various combinations of implementations are possible, and that in working with data streams, care must be taken in using overlap-save and overlap-add sectioning procedures for proper frequency domain implementations.

The development of a block state-structure with minimum round-off noise subject to ℓ2-norm dynamic range constraint is outlined. The pertinent equations for scaling and for round-off noise analysis of block-state structures are first derived. Next, a lower bound and the global minimum of the output noise due to the round-off of the block-state variables are derived. A method of deriving the minimum round-off noise block state-structure is outlined. A numerical example is included. With regard to computational complexity and overall noise performance, the block state realization of recursive digital filters is shown to be superior.

A microprocessor-based digital filter laboratory station to provide hands-on experience to the students in the design of digital filters is described. The unit is centered around an 8080A microprocessor which can be employed programmatically by the user to interconnect the various modules comprising a digital filter and to experimentally evaluate their characteristics. This flexible laboratory station allows the student to conduct a variety of experiments in the fundamentals of digital signal processing and introductory digital filter design based on the Peled-Liu (Croisier et-al) algorithm.

This paper presents a formal procedure for determining the state space representations of any digital network consisting of adders, multipliers and delays. Such representations are called state-structures whenever the state variables are exclusively identified to the appropriately chosen internal node variables of the network. In general, the state-structures corresponding to a given network are not unique, and for non-canonic networks, it is sometimes possible to find state-structures for state vectors of the lowest dimension. Procedures for determining such minimal structures are also discussed.

A normalized digital two-pair has unity Lp- scaling norms at all pertinent internal nodes and the two output nodes. A simple technique is proposed to derive the normalized filter structure recently forwarded by Gray and Markel. Additional normalized digital two-pairs are also derived.

A general scheme for implementing a two-dimensional FIR filter using only one multiplier is outlined. The realization is based on sequentially multiplexing the multiplier inputs and is illustrated with the aid of a block diagram and the sequence of operations for a 3 x 3 filter.

It is shown that a second-order digital notch filter is uniquely characterized by two distinct parameters, the notch frequency and the 3-dB rejection bandwidth. As a result, such a filter can be realized using only two multipliers. Methods are outlined to design a notch filter for a prescribed notch frequency and a prescribed 3-dB rejection bandwidth, along with procedures for postdesign adjustment of these parameters. All two-multiplier, canonic and noncanonic, notch filter configurations are developed using the multiplier extraction approach. These networks are then compared with regard to the effect of internal multiplication roundoff errors. Results of computer simulation of the notch filter configurations are also included.

A simple algorithm for testing the 2-summability of Boolean functions is presented in this note. The concept of asummobility has been extended and the idea of "mutual 2-asummability" has been introduced. The authors show how mutual 2-asummobility can be utilized for the testing of isobaricity of threshold functions containing no more than seven variables.