Clock jitter plays an important role in A/D and D/A conversions. Various aspects of this problem have been extensively studied. We consider here the effect of clock jitters in the basic system of digital filtering of analog signals. The system consists of an A/D, followed by a digital filter, and then followed by a hold circuit for D/A reconstruction. Thus the readout jitter affects both the leading edge and the trailing edge of the rectangular pulse in the reconstruction. This system includes the familiar sampling of an analog signal and subsequent reconstruction from its samples. Expressions are derived for the mean squared error caused by the sampling clock jitter and readout clock jitters. Expressions are also derived showing how the signal spectra are modified by clock jitters.

A method to accurately align plane curves related by projective transform is described in this paper. Superior accuracy and efficiency are achieved by the use of super-curve and B-spline fusion. A super-curve is formed by superimposing two transform related and aligned curves upon each other. The B-spline fusion technique uses a single B-spline to approximate the super-curve and to align the two curves at the same time. The eight-parameter projective transform is decomposed into a simple two-parameter projective transform and an affine transform, for which a linear solution can be found. Therefore the search in the traditional eight dimensional space is reduced to a two dimensional search. The major contribution of the paper lies in the novel use of a single B-spline to represent two curves, whereas in previous approaches each curve is represented with a separate B-spline. This use of a single B-spline gives higher resolution from the two point sets instead of one. So the final result is more robustness to sampling noise. It also provides a simple and integrated framework in solving the curve matching and the transform recovery problems simultaneously.

Two algorithms are presented for the detection of gradual transitions in video sequences. The first is a dissolve detection algorithm utilizing certain properties of a dissolve's trajectory in image-space. It is implemented both as a simple threshold-based detector, and as a parametric detector by modeling the error properties of the extracted statistics. The second is an algorithm to detect a wide variety of wipes based on image histogram characteristics during such transitions. Both algorithms operate in the compressed domain, requiring only partial decoding of the compressed video stream. Experiments show the algorithms perform as well as-and in some cases, better than-full-frame methods, on a wide variety of gradual transitions, and can operate significantly faster than real-time.

Accurate foreground segmentation is a difficult task due to factors such as illumination variation, occlusion, background movement, and noise. We present a novel adaptive transform domain approach for foreground segmentation in video sequences. A set of DCT-based features is employed to exploit the spatial and temporal correlation in the video sequences. We maintain an adaptive background model and make a decision based on the distance between the features of the current frame and that of the background model. Additional higher level processing is employed to deal with the variation of the environment and to improve the accuracy of segmentation. The approach is shown to be insensitive to illumination change and to noise. It also overcomes many common difficulties of segmentation such as foreground aperture and moved background objects. The algorithm can perform in real-time.

Network routing in wireless ad hoc networks is liable to attacks that may have a grave impact on network operations. Such attacks can be targeted at the route discovery process or the data packet forwarding process. Although the protection of route discovery is a critical prerequisite to ensure the robustness of the routing process, secured route discovery by no means eliminates attacks on routing. We, accordingly, propose a secure data forwarding protocol that detects faulty links in the packet forwarding process, which enables the corresponding sources to progressively route packets over non-faulty paths.

In this paper, we present an unbalanced key establishment scheme for a heterogeneous wireless network environment. We use powerful access points as multiple security managers to configure low-end reduced functional devices (RFD) on site. Our scheme is proposed to set up the master key between a roaming RFD node and a security manager during the handoff process, which exploits the difference in device capabilities, and puts the cryptographic burden where resources are less constrained. The scheme authenticates the device identities in a flexible manner, based on asymmetric certificates. A TESLA certificate is deployed to enable efficient certificate verification on RFD nodes. Our protocol offloads the expensive public key operations from the low-end RFD nodes to powerful security managers, and has less computation complexity than all the other authenticated key agreement protocols that adopt elliptic curve cryptography.

We solve the 2-D affine image registration problem by curve matching and alignment. Our approach starts with a super-curve, which is formed by superimposing two affine related curves in one coordinate system. We use B-spline fusion technique to find a single B-spline approximation of the super-curve and a registration between the two curves simultaneously. This approach achieves superior accuracy and efficiency in curve matching and alignment. We then address the occlusion problem by finding partial match between the curves segmented using inflections and cusps, which are affine invariant. The combination of edge detection and curve alignment lead to accurate image registration.

This paper proposes a new method to embed data in binary images, including scanned text, figures, and signatures. The method manipulates "flippable" pixels to enforce specific block-based relationship in order to embed a significant amount of data without causing noticeable artifacts. Shuffling is applied before embedding to equalize the uneven embedding capacity from region to region. The hidden data can be extracted without using the original image, and can also be accurately extracted after high quality printing and scanning with the help of a few registration marks. The proposed data embedding method can be used to detect unauthorized use of a digitized signature, and annotate or authenticate binary documents. The paper also presents analysis and discussions on robustness and security issues.

An affine invariant 2D curve matching and alignment approach is proposed to solve the image registration problem. Superior accuracy and efficiency is achieved by a concept called super-resolution curve and a technique called B-spline fusion. A super-resolution curve is formed by superimposing two affine related and registered curves (in discrete form) upon each other. The B-spline fusion technique is designed to obtain a single B-spline approximation of the super-resolution curve and registration estimate simultaneously. Occlusion is handled by curve segmentation using inflections and cusps, which are affine invariant. Partial match then becomes possible by matching segments of curves. A complete image registration framework based on edge detection and curve alignment is then proposed. Accurate registration results have been achieved.

The appearance of an object can be severely affected by illumination. Thus, illumination correction is necessary both for human perception and machine recognition. The paper reports on a general approach for fast illumination correction. The approach has been tested for application in face normalization as a preprocessing step in face recognition. The basic idea of the algorithm is to normalize the image contrast locally using an affine transformation lighting model based on local estimation of background and gain. The background is estimated via an efficient multi-resolution low-pass filter and the gain is estimated via homomorphic filtering. This is followed by normalizing the data with the help of a clipped histogram. Experiments on images with different lighting conditions produce results that are better than those from using several popular illumination correction methods.

Time-sensitive mobile commerce is vulnerable to message authentication delays. Significant power consumption incurred by cryptography is another limiting factor of most mobile devices. In this paper, we present a scalable mobile cryptosystem, which installs a group key and an elliptic curve private/public key pair in each device to enable both symmetric key and public key cryptography. Scalable key establishment protocols and secure routing protocols with scalable authentication are proposed to make tradeoffs between security and energy, according to different mobile applications.

In this Part I of a two-part paper, we address a number of fundamental issues of data hiding in image and video and propose general solutions to them. We begin with a review of two major types of embedding, based on which we propose a new multilevel embedding framework to allow the amount of extractable data to be adaptive according to the actual noise condition. We then study the issues of hiding multiple bits through a comparison of various modulation and multiplexing techniques. Finally, the nonstationary nature of visual signals leads to highly uneven distribution of embedding capacity and causes difficulty in data hiding. We propose an adaptive solution switching between using constant embedding rate with shuffling and using variable embedding rate with embedded control bits. We verify the effectiveness of our proposed solutions through analysis and simulation. And Part II will apply these solutions to specific design problems for embedding data in grayscale and color images and video.

This paper applies the solutions to the fundamental issues addressed in Part I to specific design problems of embedding data in image and video. We apply multilevel embedding to allow the amount of embedded information that can be reliably extracted to be adaptive with respect to the actual noise conditions. When extending the multilevel embedding to video, we propose strategies for handling uneven embedding capacity from region to region within a frame as well as from frame to frame. We also embed control information to facilitate the accurate extraction of the user data payload and to combat such distortions as frame jitter. The proposed algorithm can be used for a variety of applications such as copy control, access control, robust annotation, and content-based authentication.

This paper discusses the problem of reduced-resolution transcoding of compressed video bitstreams. An analysis of drift errors is provided to identify the sources of quality degradation when transcoding to a lower spatial resolution. Two types of drift error are considered: a reference picture error, which has been identified in previous works, and error due to the noncommutative property of motion compensation and down-sampling, which is unique to this work. To overcome these sources of error, four novel architectures are presented. One architecture attempts to compensate for the reference picture error in the reduced resolution, while another architecture attempts to do the same in the original resolution. We present a third architecture that attempts to eliminate the second type of drift error and a final architecture that relies on an intrablock refresh method to compensate for all types of errors. In all of these architectures, a variety of macroblock level conversions are required, such as motion vector mapping and texture down-sampling. These conversions are discussed in detail. Another important issue for the transcoder is rate control. This is especially important for the intra-refresh architecture since it must find a balance between number of intrablocks used to compensate for errors and the associated rate-distortion characteristics of the low-resolution signal. The complexity and quality of the architectures are compared. Based on the results, we find that the intra-refresh architecture offers the best tradeoff between quality and complexity and is also the most flexible.

This paper explains and analyzes the successful attacks submitted by the authors on four audio watermark proposals during a 3-week SDMI public challenge. Our analysis points out some weaknesses in the watermark techniques currently under SDMI consideration and suggests directions for further improvement. The paper also discusses the framework and strategies for analyzing the robustness and security of watermarking systems as well as the difficulty, uniqueness, and unrealistic expectations of the attack setup.

Compression on a watermarked image can significantly affect the detection of the embedded watermark. To show that a particular watermarking scheme is robust against compression, simulation is often relied upon. In this paper, we investigate this problem analytically. We first characterize the noise introduced by JPEG compression. We then propose a maximum a posteriori (MAP) detector, analyze its performance, and demonstrate that it has superior performance over the correlation detector.

Error concealment plays an important role in combating transmission errors. Methods of error concealment that produce better quality are generally of higher complexity, thus making some of the more sophisticated algorithms not suitable for real-time applications or restricted to client devices with limited capability. We propose an approach to use data hiding to facilitate the error concealment at the decoder. A set of features are extracted at the encoder and embedded imperceptibly into the host media. If some part of the media data is damaged during the transmission, the embedded features can be extracted and used for recovery of lost data. The use of data hiding leads to reduced complexity at the decoder. Simulation shows that our approach has better image quality than some well-known conventional error concealment methods.

Two algorithms are presented for the detection of gradual transitions in video sequences. The first is a dissolve detection algorithm utilizing certain properties of a dissolve's trajectory in image-space. The second is an algorithm to detect a wide variety of wipes based on the image histogram characteristics during such transitions. Both algorithms operate in the compressed domain, requiring only partial decoding of the compressed video stream. Experiments show the algorithms perform well in detecting a wide variety of gradual transitions, and at a significant reduction in computation time when compared with full-frame methods.

In network delivery of digital video, if the bandwidth required for a video is not available, the video has to be recoded at a reduced bit rate. It is highly desirable that the transcoding is carried out in real time while maintaining reasonable image quality. In this paper, we propose a fast approach to derive from an MPEG stream a new MPEG stream with half the spatial resolution. For the downsized video, we first generate from the original compressed video an improved estimate of the motion vectors. We then propose a compressed domain approach with data hiding to produce DCT residues by an open-loop method. The computational complexity is significantly lower than a number of previous approaches. Simulation suggests that our approach produces reasonable image quality.

This paper applies shuffling to digital watermarking and data hiding. The data embedding capacity in the multimedia source generally varies significantly from one part of the source to another. Sequential embedding is very sensitive to noise which may cause synchronization problem; the common but conservative solution via partitioning an image into large segments and embedding only one bit per segment is wasteful of the data embedding capacity. This paper shows how random shuffling can be used to equalize the uneven distribution of embedding capacity. The effectiveness of random shuffling is demonstrated by analysis and experiments.

This paper first proposes a computationally efficient spatial directional interpolation scheme, which makes use of the local geometric information extracted from the surrounding blocks. The proposed error-concealment scheme produces results that are superior to those of other approaches, in terms of both peak signal-to-noise ratio and visual quality. Then a novel approach that incorporates this directional spatial interpolation at the receiver is proposed for block-based low-bit-rate coding. The key observation is that the directional spatial interpolation at the receiver can reconstruct faithfully a large percentage of the blocks that are intentionally not sent. A rate-distortion optimal way to drop the blocks is shown. The new approach can be made compatible with standard JPEG and MPEG decoders. The block-dropping approach also has an important application for dynamic rate shaping in transmitting precompressed videos over channels of dynamic bandwidth. Experimental results show that the proposed coding and rate-shaping systems can provide significant subjective and objective gains over conventional approaches.

Digital watermarking has been proposed as the means for copyright protection of multimedia data. Many of existing watermarking schemes focused on the robust means to mark an image invisibly without really addressing the ends of these schemes. This paper first discusses some scenarios in which many current watermarking schemes fail to resolve the rightful ownership of an image. The key problems are then identified, and some crucial requirements for a valid invisible watermark detection are discussed. In particular, we show that, for the particular application of resolving rightful ownership using invisible watermarks, it might be crucial to require that the original image not be directly involved in the watermark detection process. A general framework for validly detecting the invisible watermarks is then proposed. Some requirements on the claimed signature/watermarks to be used for detection are discussed to prevent the existence of any counterfeit scheme. The optimal detection strategy within the framework is derived. We show the effectiveness of this technique based on some visual-model-based watermark encoding schemes.

A data embedding method is proposed for image authentication based on table look-up in frequency domain. A visually meaningful watermark and a set of simple features are embedded invisibly in the marked image, which can be stored in the compressed form. The scheme can detect and localize alterations of the original image, such as the tampering of images exported from a digital camera.

The detection of transitions between shots in video programs is an important first step in analyzing video content. The wipe is a frequently used transitional form between shots. Wipe detection is more involved than the detection of abrupt and other gradual transitions because a wipe may take various patterns and because of the difficulty in discriminating a wipe from object and camera motion. In this paper, we propose an algorithm for detecting wipes using both structural and statistical information. The algorithm can effectively detect most wipes used in current TV programs. It uses the DC sequence which can be easily extracted from the MPEG stream without full decompression.

Digital watermarking has been proposed as a means for copyright protection of multimedia data. This paper first discusses some scenarios in which many current watermarking schemes fail to resolve the rightful ownership of an image. We then identify the key problems and discuss some crucial requirements for a valid invisible watermark detection. In particular, we argue that, for the particular application of resolving rightful ownership using invisible watermarks, it might be crucial to require that the original image not be directly involved in the watermark detection process. A general framework for validly detecting the invisible watermarks is then proposed. We show the effectiveness of this technique based on some visual-model-based watermarking schemes.

Rate shaping plays an important role in transmitting compressed video on a network with dynamic bandwidth. We present a scheme for rate shaping JPEG/MPEG-pre-compressed image/video with feature analysis in scale space. The proposed scheme draws its strengths from a technique for identifying perceptually important features based on geometry-driven diffusion, an interpolation scheme allowing many intentionally dropped blocks to be recovered faithfully from neighboring transmitted blocks, and some careful observations about the close interactions between block dropping and feature analysis. Compared with a successful rate shaping scheme based on joint block dropping and uniform coefficient truncation, the new scheme not only produces images of significantly higher visual quality, but also better PSNR at low bit rates.

A novel approach which combines directional spatial interpolation at the receiver and block-based coding is proposed for low bit rate coding. The directional spatial interpolation at the receiver can reconstruct faithfully a large percentage of the blocks that are intentionally not sent. Experimental results show that the new proposed coding system can provide significant subjective and objective gains over conventional approaches for still image compression, and has the potential to be extended for video coding.

In the transmission of a precoded, stored video such as that in video-on-demand systems , it is often necessary to reduce the bit rate of the compressed video in cases that the network capacity is reduced. This paper proposes a novel block-dropping approach for rate shaping of MPEG-precompressed video. A directional spatial interpolation scheme is incorporated at the receiver to reconstruct faithfully a large percentage of the blocks that are intelligently dropped to meet the constraint of reduced bandwidth. The blocks are dropped in a way that is optimal in the rate-distortion sense. The new approach is conceptually quite different from conventional approaches in which coefficients (usually high frequency coefficients) are eliminated. Experimental results show that the proposed scheme can provide significantly higher peak signal-to-noise ratio (PSNR) and much better visual quality than conventional approaches. We also show that by jointly dropping blocks and coefficients, the bit rate...

For MPEG video coding and recording applications, it is important to select the quantization parameters at slice and macroblock levels to produce consistent quality image for a given bit budget. A well-designed rate control strategy can improve the overall image quality for video transmission over a constant-bit-rate channel and fulfil the editing requirement of video recording, where a certain number of new pictures are encoded to replace consecutive frames on the storage media using, at most, the same number of bits. We developed a feedback re-encoding method with a rate-quantization model, which can be adapted to changes in picture activities. The model is used for quantization parameter selection at the frame and slice level. The extra computations needed are modest. Experiments show the accuracy of the model and the effectiveness of the proposed rate control method. A new bit allocation algorithm is then proposed for MPEG video coding.

We consider a new problem in tomographic imaging. In a sequence of transverse images, adjacent slices often look similar to each other. We investigate the possibility of using this correlation to help reconstruct the sequence with 2-D in-plane data. The problem is formulated as a maximum a posteriori (MAP) estimation problem, using an edge-preserving Markov random field prior model. Both Gaussian and Poisson data are considered. Some improvements over the single-slice MAP reconstructions are observed.

We consider tomographic image reconstruction from a limited number of noisy projections. An efficient algorithm based on maximum likelihood estimation (MLE) is developed to reconstruct images of multiple discs with unknown locations and radii. The algorithm is successfully applied to images with signal-to-noise ratio (SNR) as low as 0 dB, using as few as 16 projections, and containing as many as twelve discs with widely varying radii. Experimental results show that our approach significantly outperforms conventional convolution back projection. The algorithm is successfully extended to the multiple ellipse case.

Presents a new interframe coding method for medical images, in particular magnetic resonance (MR) images. Until now, attempts in using interframe redundancies for coding MR images have been unsuccessful. The authors believe that the main reason for this is twofold: unsuitable interframe estimation models and the thermal noise inherent in magnetic resonance imaging (MRI). The interframe model used here is a continuous affine mapping based on (and optimized by) deforming triangles. The inherent noise of MRI is dealt with by using a median filter within the estimation loop. The residue frames are quantized with a zero-tree wavelet coder, which includes arithmetic entropy coding. This particular method of quantization allows for progressive transmission, which aside from avoiding buffer control problems is very attractive in medical imaging applications.

Discrete cosine transform coding, a popular image compression strategy, results in two visible artifacts: blocking and ringing. These are both high frequency artifacts. Since images contain high frequency information the artifacts are removed using a space varying low pass filter as a post processor. Low frequency blocks and flat regions of blocks containing a strong edge are filtered. Low frequency blocks are identified in the transform coefficient domain; edge blocks are identified in the spatial domain. This does not require any alterations in the compressed bit stream. Improvement is demonstrated both subjectively and objectively.

Reduced images formed from the collection of DC coefficients in intra-coded DCT compressed video retain a "global" feature which is useful for processing purposes. This paper examines the direct reconstruction of such DC images from motion-compensated P-frames and B-frames of MPEG compressed video. Exact expressions are derived and approximations are given for the computational speedup. The analysis and experimental results show that the approximations yield images that are very close to the true ones.

Browsing, search and retrieval in digital video libraries depend on the ability of the system to match, classify and group video shots by their visual contents. However, similarity of shots cannot always be settled by using only one key frame per shot as commonly practiced. In this paper we propose a scheme to match video shots and to cluster them by taking into account the temporal variations within individual shots. A much reduced representation for a video shot is used. These images still capture the dynamics of visual contents for matching and clustering process. Experimental results are reported.

Several rapid scene analysis algorithms for detecting scene changes and flashlight scenes directly on compressed video are proposed. These algorithms operate on the DC sequence which can be readily extracted from video compressed using Motion JPEG or MPEG without full-frame decompression. The DC images occupy only a small fraction of the original data size while retaining most of the essential "global" information. Operating on these images offers a significant computation saving. Experimental results show that the proposed algorithms are fast and effective in detecting abrupt scene changes, gradual transitions including fade-ins and fade-outs, flashlight scenes and in deriving intrashot variations.

The paper proposes a scheme to perform volume rendering from compressed scalar data. Instead of decompressing the entire data set before rendering, blocks of data are decompressed as needed. Discrete cosine transform based compression technique is used to illustrate the method. The data is partitioned into overlapping blocks to permit local rendering and allow easy parallelization. Compression by factor of 20 to 30 produces rendering virtually indistinguishable from rendering using the original uncompressed data. Speedup is obtained by making use of spatial homogeneity detected in the transform domain. Rendering time using the proposed approach is less than that of direct rendering from the entire uncompressed data. The proposed method thus offers an attractive option to reduce storage, computation, and transmission overhead of otherwise huge data sets.>

Bit rate control is an important step in the video encoding process in that it transforms a variable rate bit stream into a constant rate one for communication channels or storage of fixed bandwidth. The authors propose a hierarchical approach to this problem based on a novel method to characterize the activity or complexity of the image sequence. They introduce a local discrepancy measure, AME (average of maximum 10% of mean square error) of the macroblock. The method performs better than the others in AME with similar mean square error per pixel.>

Transform based image compression has difficulty with image regions containing edges. Edge compensated transform coding (ECTC) addresses this problem by preprocessing to remove edges. This preprocessing is adapted to transform coding. The edge information is sent in a side channel and the edges are replaced at the receiver. Subjective improvement is demonstrated.>

We present a new inter-frame coding for medical images, in particular magnetic resonance (MR) images. Until now, attempts in using inter-frame redundancies for coding MR images have been unsuccessful. We contend that the main reason for this is twofold: bad inter-frame estimation models and ignoring the thermal noise inherent in MRI. Our inter-frame model is a continuous affine mapping based on (and optimized by) deforming triangles. The inherent noise of MRI is dealt with by using a median filter within the estimation loop. Simulations demonstrate the viability of this algorithm.>

Considers the problem of tomographic image reconstruction from a limited number of noisy projections. Maximum likelihood estimation is used to reconstruct an image of multiple discs with unknown locations and radii. An efficient algorithm is developed to tackle the computation. The algorithm is successfully applied to images containing as many as twelve discs with widely varying radii and with signal-to-noise ratio as low as 0 dB, and the number of projections used is as few as 16. Experimental results show that the approach significantly outperforms the conventional convolution back-projection method.>

Two algorithms for block motion estimation that produce performance similar to that of exhaustive search but with computation reduced by a factor of 8 or 16 are presented. The algorithms are based on motion-field and pixel subsampling. A subsampled motion field is first determined by estimating the motion vectors for a fraction of the blocks. The motion vectors for these blocks are determined by using only a fraction of the pixels at any searched location and by alternating the pixel subsampling patterns with the searched locations. The subsampled motion field is then interpolated so that a motion vector is determined for each block of pixels. The algorithms are more robust than previously proposed fast algorithms and both can easily be combined with a hierarchical search strategy. One of the algorithms is fully compatible with MPEG-I.>

An approach to the lossy compression of color images with limited palette that does not require color quantization of the decoded image is presented. The algorithm is particularly suited for coding images using an image-dependent palette. The technique restricts the pixels of the decoded image to take values only in the original palette. Thus, the decoded image can be readily displayed without having to be quantized. For comparable quality and bit rates, the technique significantly reduces the decoder computational complexity.

The implementation of digital signal processing algorithms often requires that a variety of conflicting criteria be satisfied. A signal processing system must provide the necessary processing gains, while various measures of the feasibility and efficiency of implementation, such as power and cost, are met. This paper reviews the motivation behind the development of low power signal processing algorithms, presents some methods for addressing these problems, and gives several examples of reduced complexity signal processing implementations.>

Two fast algorithms are presented to reduce the computational complexity of block motion estimation. Previously proposed fast algorithms reduce the number of computations by limiting the number of locations that are searched to find the motion vectors of each block. The techniques presented use block and pixel subsampling to reduce the number of computations of block motion estimation. Because an exhaustive search is used to estimate a fraction of the motion vectors, these techniques are more robust than those previously proposed. Alternating the pixel subsampling patterns with the searched locations minimizes the effects of the aliasing that is introduced by subsampling the pixels without prior low-pass filtering. Block and pixel subsampling by a factor of four each reduce the computational complexity of block motion estimation by a factor of 16. Performance similar to full exhaustive search is obtained.>

The implementation of signal processing algorithms on a heterogeneous multiprocessor system is examined. The signal processing algorithm, represented as a directed signal flow graph, is mapped to the multiprocessor system for execution. A heuristic scheme aimed at producing a schedule of minimum execution time is proposed. Communication overhead is incorporated in the scheduling. Simulation results are presented using both the proposed heuristic scheme and an optimum scheme based on the branch-and-bound approach. The heuristic results fall within a reasonable range from the optimal schedule.>

Adaptive smoothing filters have been studied for the removal of narrow-band interference and for use in spectral estimation. The authors study the convergence of two LMS (least mean square) adaptive smoothers, one constrained to have symmetry, the other with each tap adapting independently. Since the behavior of the adaptive filters is dependent upon the characteristics of the signal on the filter taps, the authors explore differences in convergence among these two smoothing algorithms and the LMS predictor through this signal vector. By analyzing in detail this behavior for a sinusoid in white noise, they show that if the sinusoid is neither very low nor high in frequency then the constrained smoother has both better convergence and steady-state behavior than either the predictor or the unconstrained smoother while requiring one-half as many multiplications.>

An approach for the compression of color images with limited palette size that does not require color quantization of the decoded image is presented. The technique restricts the pixels of the decoded image to take values only in the original palette. Thus, the decoded image can be readily displayed without having to be quantized. Results obtained with a typical image are included to compare a conventional coding scheme to the proposed one. For comparable quality and bit rates, the proposed technique significantly reduces the decoder computational complexity.>

A multiple resolution algorithm is presented for segmenting images into regions with differing statistical behavior. In addition, an algorithm is developed for determining the number of statistically distinct regions in an image and estimating the parameters of those regions. Both algorithms use a causal Gaussian autoregressive model to describe the mean, variance, and spatial correlation of the image textures. Together, the algorithms can be used to perform unsupervised texture segmentation. The multiple resolution segmentation algorithm first segments images at coarse resolution and then progresses to finer resolutions until individual pixels are classified. This method results in accurate segmentations and requires significantly less computation than some previously known methods. The field containing the classification of each pixel in the image is modeled as a Markov random field. Segmentation at each resolution is then performed by maximizing the a posteriori probability of this field subject to the resolution constraint. At each resolution, the a posteriori probability is maximized by a deterministic greedy algorithm which iteratively chooses the classification of individual pixels or pixel blocks. The unsupervised parameter estimation algorithm determines both the number of textures and their parameters by minimizing a global criterion based on the AIC information criterion. Clusters corresponding to the individual textures are formed by alternately estimating the cluster parameters and repartitioning the data into those clusters. Concurrently, the number of distinct textures is estimated by combining clusters until a minimum of the criterion is reached.>

A method of estimating both the number and type of textures in an image is proposed. An autoregressive (AR) texture model is used since it describes spatial behavior in addition to mean and local variation. Solution criteria are formulated based on the concurrent estimation of the number of textures, the texture parameters, and the class of texture samples. This approach avoids problems with the instability of maximum likelihood estimation and results in an algorithm which is composed of three basic operations. The first two operations alternately reestimate the texture parameters and repartition the data into the clusters corresponding to individual textures. The third operation agglomerates clusters to reduce the number of distinct textures. Each operation attempts to minimize the basic solution criteria.>

The implementation of a high-speed, programmable finite impulse response (FIR) filter using coefficients consisting of two power-of-two terms is presented. The area and speed performance figures for this application-specific IC (ASIC) demonstrate the superiority of this architecture for high-speed and high-density implementation. This implementation was developed using a relatively primitive CMOS process. Simple lambda -rule scaling suggests that by using a 1.25- mu m and double-level metal process of the same die size, this architecture will allow the implementation of a filter of approximately 200 taps operating at a 10-MHz sampling rate.>

An algorithm which approximates the maximum likelihood estimator (MLE) for the locations of constant-density discs in integral projection data is presented. The algorithm is of linear complexity in the object count and requires only approximately 25% more computation than the MLE of the single-location problem. Approximation error analysis, in terms of error probability, is provided through empirical matching of densities for the extremal values of the random-noise field.>

The authors consider the implementation of the combined variable-step-size (VS)-power-of-two quantizer-multiplier (PTQ) algorithm in a 2.5- mu m CMOS process. A 7-MHz chip with four taps, using dedicated hardware for each tap, and a 32-kHz chip with 63 taps, using multiplexed processing hardware, are presented. The area and speed performance figures for these chips are comparable with recently published results when lambda -rule scaling is used; however, the performance of the VS-PTQ algorithm is superior.>

The authors discuss a way to improve transmission tomograms in the presence of large density data variations and low photon dosage. They present a design for nonstationary filters that exploits the detectability of high-density regions in the object to match filters to local noise properties. The design of each filter is formulated as a least-squares optimization problem, with linear equality and inequality constraints that protect the resolution of detail while minimizing noise power in the reconstruction. Experimental results show reconstructions in whitened noise of power equivalent to those of conventional convolution backprojection, but with significantly better resolution.>

A method is presented for segmenting images into a discrete set of classes by first segmenting at low resolution and then progressing to finer resolutions until individual pixels are classified. This multiple resolution method results in accurate segmentations and requires significantly less computation than some previously known methods. The segmentation algorithm used at each resolution is based on maximum a posteriori estimation of the field of pixel classifications, which is modeled as a Markov random field. The maximization is performed by a deterministic greedy algorithm which iteratively chooses the classification of individual pixels or blocks of pixels. A texture model is also developed which allows the extraction of a texture statistic for each pixel and is well suited for use with the proposed algorithm. Measurements of algorithm performance under varying conditions of region size and signal-to-noise ratio are presented.>

When an FIR (finite-impulse response) filter with discrete valued coefficients is implemented in direct form, the peak of the amplitude response decreases with increasing filter length, but only up to certain length. Further reduction in peak ripple beyond that point cannot be realized easily without increasing the coefficient precision. It is shown that by cascading two direct-form FIR filters, each with coefficients that are sum or difference of two power-of-two terms, it is possible to achieve very small peak ripple.>

The adaptive line enhancer (ALE) has been applied to a variety of problems. There has been extensive analysis of the convergence, tracking, and steady state error properties of the normal ALE. Recently, the effects of tap failures on the steady state error of the ALE were investigated. Here the effect of tap failure on the mean convergence behavior of the ALE operating under general tap failure is analyzed under the independence assumption. The convergence rate is shown to be related to one of the eigenvalues of the modified autocorrelation matrix. These results are then applied to the special cases of single complex exponential, single real sinusoid, and multiple complex exponential input signals in additive white noise. Simulation results showing close agreement with theory are presented.

A continuous time Markov chain model of asynchronous, nonpersistent CSMA/CD networks is developed which allows their complete characterization by a matrix whose dimensions are independent of the number of users in the network. The model provides an efficient reeursive algorithm for computing the performance of finite population networks. It also allows many analytical results to be obtained when an infinite population and a constant load retransmission policy are considered. These analytic results include necessary and sufficient conditions for stability, the distribution of the number of busy users, an exact closed form expression for the expected delay, and the exact upper bound on the throughput-all obtained via the properties of the matrix mentioned above. The results on stability show that, for this CSMA/CD model, the definitions of stability in terms of expected drift, nonnull recurrence, and maximum possible throughput exceeding actual loading are all equivalent. The model can approximate as closely as desired any distribution for the packet length, transmission detection time, and collision truncation time. Taking advantage of this freedom, the performance of CSMA/CD networks is shown to be very sensitive to the distribution of the transmission detection time.

The performance of a simplified adaptive algorithm using finite-bit power-ef-two quantizer is analyzed by assuming Gaussian distributions for both input signals and equalizer output errors. The results show that in spite of its simple implementation, the performance is comparable with the least mean square (LMS) algorithm. The convergence and the stability is then studied, the output mean square error is analyzed and the effects of non-Gaussian cases are considered. Cemputer simulation results support the theoretical results.

A new iterative method of finding the minimum eigenvalue of a symmetric matrix is described. This method does not utilize matrix inversions and is applicable to any matrix R for which the matrix-vector product Rx is rapidly computable. It seeks the minimum eigenvalue of R by minimizing the quadratic form XTRx on the unit hypersphere, using a search technique derived from the conjugate gradient method. The computational complexity of each step of the algorithm depends on the speed with which Rx can be computed.

The problem of extrapolating a band-limited signal in discrete-time is viewed as one of solving an underdetermined system of linear equations. The matrix to be inverted is also generally ill-conditioned. Singular value decomposition (SVD) provides both a means for implementing the inverse and a method for improving the numerical stability of the problem. An expression for the mean-square error incurred in solving a system of linear equations via SVD is derived. This expression can be used to estimate the number of singular values needed to form the inverse. Further examination of the expression indicates that, in the case of an oversampled signal, decimation can be applied without significantly degrading the extrapolation. The results developed for the one-dimensional case can be extended to higher dimensions, as illustrated by the two-dimensional case. Examples of the SVD approach to extrapolation are given, along with examples using other extrapolation techniques for comparison. The SVD approach is seen to yield the best extrapolation of the known minimum-norm least-squares methods.

This paper is concerned with spectral estimation of a finite number of two dimensional sinusoids embedded in white noise. Closed form expressions are derived for estimates using the autoregressive (AR) prediction error filter approach, as well as using periodogram with Bartlett window, and the maximum likelihood (ML) method. These expressions are useful in the study of resolving closely spaced sinusoidal signals. Over a narrow frequency band, direct decimation can be applied to improve resolution and/or to reduce computation. simulation results demonstrate that decimation by (D1,D2) with a support size (N1,N2) yields approximately the same resolution as a support size (D1N1,D2N2) used with the undecimated signal. The use of decimation also reduces significantly computation.

The steady state output error of the Least Mean Square (LMS) Adaptive Algorithm due to the finite precision arithmetic of a digital processor is analyzed. It is found to consist of three terms: (1) the error due to the input data quantization, (2) the error due to the rounding of the arithmetic operations in calculating the filter's output, and (3) the error due to the deviation of the filter's coefficients from the values they take when infinite precision arithmetic is used. The last term is inversely proportional to the adaptation step size µ. Both fixed and floating point arithmetics are examined. The relation between the quantization error and the error that occurs when adaptation possibly ceases due to quantization is also investigated.

This paper presents an investigation of the resolution of Autoregressive (AR) spectral analysis. An expression for the Mth-order exact AR spectrum for K complex sinusoids with additive white noise is derived. In order to relate the resolution to the model order and signal power, the resolution boundary is defined for two-sinusoids in white noise. Empirical formulas are given relating resolution to the factors affecting it.

A continuous time Markov chain model of a nonpersistent carrier sense multiple access with collision detection (CSMA/CD) protocol is developed to determine the performance of finite population systems. The model allows a wide range of distributions for the length of packets and the lengths of the transmission detection and collision detection times. A stability measure for finite population asynchronous systems-the instantaneous expected drift-is developed. Performance calculations for many sample systems show that the following behavior is characteristic of these systems: a wide range of retransmission rates provides almost optimal performance; the instantaneous drift is a sensitive indicator of the stability characteristics of CSMA/CD networks; if high fixed retransmission rates are used, performance decays very rapidly when other network parameters cross critical thresholds. In addition, adaptive retransmission policies and the maximum length of a CSMA/CD cable network are found to be very sensitive to the distribution of the transmission detection time.

The well-known decimation-in-time and decimation-infrequency FFT algorithms have recently been combined into a single and more efficient one, the Mixed Decimation FFT algorithm. On the other hand, an efficient way to perform a two dimensional DFT computation is to use decimation-in-time or decimation-infrequency in both dimensions simultaneously. In this paper the above two ideas are combined to give a new two dimensional DFT algorithm, the Mixed Simultaneous Decimation FFT algorithm.

A new scheme for a transmultiplexer is described. Using the polyphase network approach a filter bank composed of only all-pass digital filter sections was designed. The use of all-pass filters as basic building blocks is shown to provide a transmultiplexer structure that has low computational requirements, low quantization noise, and high modularity.

The frequency spectrum of a long dsta sequence over a narrow band can be efficiently computed by decimating the sequence using FIR filters, and calculating an FFT on the shortened output. This method offers a low computation rate, a small storage requirement, good frequency resolution, and adjustable accuracy [1]. The number of computations can be decreased for the lowpass case by relaxing the filter constraints [2]. This lowers the order of the filter necessary to attain a given level of accuracy. This paper extends the procedure proposed in [2] to bandpass filters. An algorithm is developed for choosing the best decimation rates and designing appropriate decimating filters for any chosen frequency band. The algorithm is used to derive tables of optimum decimation rates for a range of band positions and widths. The results demonstrate that direct decimation with a minimal passband constraint can improve on the results of [1].

The prime factor FFT

This paper considers the effect of the carrier phase error on the probability of error in a binary quadrature amplitude modulation (QAM) data transmission system in the presence of intersymbol interference and additive Gaussian noise. The analysis shows that there exists a threshold value of the carrier phase error such that the error probability remains almost unchanged as long as the carrier phase error is less than that threshold value, but increases rapidly once the threshold is exceeded. Good agreement between theory and computer simulations is obtained. Some practical implications of this threshold effect are discussed.

Errors due to finite wordlength can in general be quite large in narrowband recursive digital filters. It has been shown that the mean squared roundoff error may be considerably reduced by using a technique known as error spectrum shaping (ESS), which utilizes quantizer feedback. In this paper it is shown that ESS can also significantly reduce the amplitude of zero input limit cycle oscillations. A more complete analysis of the MSE is then presented, which is useful for design purposes.

The computer program of McClellan, Parks and Rabiner [1] for designing optimal (minimax) FIR filters requires the order of the filter as an input parameter. Although a reliable estimate for the lowpass case is known [2], no such estimate exists for the bandpass case. In this paper we investigate the problem of estimating the order of an optimal bandpass filter. The effects of the design specifications on filter order are studied, and a simple estimate of the filter order is presented.

The system considered here consists of a differential pulse-code modulator (DPCM) in which the quantizer is replaced by an adaptive quantizer. Adaptation is accomplished by adjusting the stepsize at every sampling instant, depending upon the magnitude of the quantization error. Quantizing noise in adaptive DPCM (ADPCM) systems falls into three categories: granularity, slope overload, and quantizer saturation. Granular noise occurs because only a finite number of levels are available to represent the analog input signal during the encoding process. Slope overload happens when the slope of the input signal increases faster than the adaptive system can follow. Quantizer saturation exists because nonoptimal decisions on step-size adjustments can lead to situations in which quantizer overload occurs without slope overload. The result is an error larger than a purely granular noise analysis would suggest. Equations for the three types of quantizing noise in ADPCM systems are derived, and computer simulations are perforated. For flatand RC-filtered Gaussian input signals, oversampled at various rates, the simulation results agree well with theoretical predictions. Comparisons indicate that the ADPCM can perform better than the best analogous nonadaptive system in terms of signal-to-quantizing-noise ratio. Furthermore, the optimal operating point for the ADPCM is much less sensitive to changes in input signal parameters and system component values than in nonadaptive systems.

This paper considers the design of a tapped delay line (TDL) equalizer from an error probability point of view. We define a new class of TDL equalizers, which includes the zero-forcing equalizer (ZFE) as a special case. Some optimal properties of the new equalizers are presented and their relationships to mean-square equalizers (MSE's) and ZFE are discussed. It is shown that, for a certain class of additive noise, some of the new equalizers result in a probability of error lower than that of the MSE.

An adaptive differential pulse code modulator (ADPCM) with a finite number of possible step-sizes and a leaky integrator in the feedback loop is considered. A zero-mean unit-ariance first-order Markov sequence is chosen as the input to thc system, and the leak parameter of the ADPCM accumulator is made equal to the intersample correlation of the input sequence. Using this fundamental structure, a method is presented for computing the exact joint probability distribution function of quantization error and step-size in ADPCM. From the joint distribution, marginal quantization error, and step-size distributions are obtained for Gauss-Markov, exponential-Markov, and uniform-Markov input signals. Empirical distributions obtained from simulations agree very well with their theoretical counterparts.

The problem of stability of an adaptive differential pulse code modulation (ADPCM) system is considered from two viewpoints. First, it is demonstrated that the step-size adaptation algorithm of a certain class of ADPCM's can be characterized by the system's response to step: function inputs. The degree of "hunting" or "oscillation" provides an indication of the deterministic stability of the algorithm, and algorithms are presented that minimize these effects. Secondly, stationary random processes with rational spectral densities are used to study stochastic stability of ADPCM. It is shown that for certain ADPCM's the time-averaged mean-absolute quantizing noise is bounded, that the joint distribution of the input and decoded output processes possesses a stationary distribution, that this joint distribution converges to the stationary distribution from an arbitrary starting point, and that the mean-absolute quantizing noise is finite under the stationary distribution.

The effect of intersymbol interference and additive noise on the performance of a digital data transmission system is considered. The data sequence is assumed to be independent and equiprobable. The additive noise is independent of the signal but is not restricted to be Gaussian. A simple lower bound, an upper bound, and a simple approximation to the upper bound, on the probability of error are derived. The approximation to the upper bound is twice the lower bound; hence, either can be taken as an approximation to the actual error probability.

article Floating Point Fast Fourier Transform Computation Using Double Precision Floating Point Accumulators Share on Authors: Tran-Thong Department of Electrical Engineering, Princeton University, Brackett Hall, Engineering Quadrangle, Princeton, NJ Department of Electrical Engineering, Princeton University, Brackett Hall, Engineering Quadrangle, Princeton, NJView Profile , Bede Liu View Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 3Issue 1March 1977 pp 54–59https://doi.org/10.1145/355719.355723Online:01 March 1977Publication History 1citation470DownloadsMetricsTotal Citations1Total Downloads470Last 12 Months15Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

The optimum design of recursive digital filters in the cascade realization with respect to the output noise is healed here by taking into account the ordering, the pole-zero pairing, and the selection of configurations of the individual sections. In the first part of this paper, the output noise variances are derived for arbitrary realized cascaded configuration employing either the fixed-point or the floating-point arithmetics. The second part presents a simple algorithm to compute the output noise variance without direct evalution of complex integral. An example is presented in which the individual sections are allowed to take on different configurations.

A recursive digital filter using differential pulse-code modulation (DPCM) is proposed. The filter can realize any rational transfer function without the need for a new design. Results on roundoff error and limit cycle oscillations are presented. The implementation of these filters is also discussed.

The present paper considers discrete time analyses of firstand second-order digital phase lock loops. These loops are characterized by the fact that they track the zero crossings of the incoming signal; consequently, the sampling intervals are nonuniform. The firstorder loop is analyzed for phase step and frequency step inputs; mean time to skip cycle is also considered. For phase step input, approximate expressions are obtained for the steady-state phase error probability density and phase error variance, the second of which leads directly to a theoretical prediction of threshold. The second-order loop is analyzed for frequency step input. Approximate expressions for the steady-state phase error probability density, phase error variance, and a theoretical prediction of threshold are obtained. The analyses are confirmed by numerical results and simulation.

A bound on the relative error in floating-point addition using a single-precision accumulator with guard digits is derived. It is shown that even with a single guard digit, the accuracy can be almost as good as that using a double-precision accumulator. A statistical model for the roundoff error in double-precision multiplication and addition is also derived. The model is confirmed by experimental measurements.

The series expansion of a bivariate distribution and the series expansion of the output of a nonlinearity are considered, as well as the relationship between these two problems. Three distinct expansions of bivariate distributions are presented along with a constructive procedure to obtain them explicitly. The cross-covarianee property and certain results on the expansion of the output of a nonlinearity are extended to a larger class of random processes.

The fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier coefficients with a substantial time saving over conventional methods. The finite word length used in the computer causes an error in computing the Fourier coefficients. This paper derives explicit expressions for the mean square error in the FFT when floating-point arithmetics are used. Upper and lower bounds for the total relative mean square error are given. The theoretical results are in good agreement with the actual error observed by taking the FFT of data sequences.

This paper presents a general approach to the derivation of series expansions of second-order wide-sense stationary mean-square continuous random process valid over an infinite-time interval. The coefficients of the expansion are orthogonal and convergence is in the mean-square sense. The method of derivation is based on the integral representation of such processes. It covers both the periodic and the aperiodic cases. A constructive procedure is presented to obtain an explicit expansion for a given spectral distribution.

This paper is devoted to a special class of linear time-varying filters, members of which are commonly employed in practice. It is shown that some of these filters share a number of desirable properties with linear stationary systems, the most important of which is the preservation of wide sense stationarity of stochastic inputs. An application to the problem of transmitting a continuous signal over a sampled data channel is included. Some results coincide with those for a multichannel system with simultaneous optimum stationary presampling and postsampling filters.

This paper treats the problem of the representation and reconstruction of signals from several sets of sampled values using a multiple-channel sampling and reconstruction scheme. Realizable and unrealizable solutions are presented for the optimum linear postfiltering and prefiltering operations. It is shown that the number of "independent" sets of samples which are necessary for the exact reconstruction of a signal is equal to the maximum number of overlappings of its sampled spectrum. This enables many different sampling expansions to be derived. The simultaneous optimization of the unrealizable linear prefilter and postfilter combination is carried out for the case where two sets of sampled values are taken. It is shown that with the optimum combination of filters, the angular frequency range of the input signal is limited by the prefilters to a total width of4\pi \rho, which is a natural extension of the single-channel result.