The optimum non‐negative integer bit allocation (ONIBA) is an important technique, which provides optimal quantisation of transform coefficients for the image transform coders (ITCs). However, the existing ONIBA algorithms are still not popular for the discrete cosine transform (DCT)‐based ITCs, due to their image‐dependent nature and additional side information requirements. Therefore, this study presents a novel image‐independent ONIBA (IIONIBA) technique to achieve efficient quantisation for the DCT‐ITCs. For the development of the proposed IIONIBA technique, initially, an image‐dependent ONIBA algorithm is proposed, which is then mapped into desired image‐independent solution via utilisation of a prepared combined image and proposed modified step size mapping technique. Thereafter, a new lookup table for the elements of quantisation tables, obtained from the proposed IIONIBA technique, is established using non‐linear regression analysis, to reduce the problem of additional side information requirements. Several experiments are performed to evaluate the performance of the proposed IIONIBA technique based on the visual quality assessment of reconstructed images and the image quality indexes peak signal to noise ratio (PSNR) and mean structural similarity index (MSSIM). The results show that the proposed IIONIBA technique delivers better quantisation and provides significant gains in the image quality indexes as compared to the recent quantisation techniques.

In medical practice, the X-ray Computed tomography-based scans expose a high radiation dose and lead to the risk of prostate or abdomen cancers. On the other hand, the low-dose CT scan can reduce radiation exposure to the patient. But the reduced radiation dose degrades image quality for human perception, and adversely affects the radiologist's diagnosis and prognosis. In this paper, we introduce a GAN based auto-encoder network to de-noise the CT images. Our network first maps CT images to low dimensional manifolds and then restore the images from its corresponding manifold representations. Our reconstruction algorithm separately calculates perceptual similarity, learns the latent feature maps, and achieves more accurate and visually pleasing reconstructions. We also showed the effectiveness of our model on a number of patient abdomen CT images, and compare our results with existing deep learning and iterative reconstruction methods. Experimental results demonstrate that our model outperforms other state-of-the-art methods in terms of PSNR, SSIM, and statistical properties of the image regions. https://github.com/ShibaPrasad/CT-Image-Reconstruction.

One of the common modalities for observing mental activity is electroencephalogram (EEG) signals. However, EEG recording is highly susceptible to various sources of noise and to inter subject differences. In order to solve these problems we present a deep recurrent neural network (RNN) architecture to learn robust features and predict the levels of cognitive load from EEG recordings. Using a deep learning approach, we first transform the EEG time series into a sequence of multispectral images which carries spatial information. Next, we train our recurrent hybrid network to learn robust representations from the sequence of frames. The proposed approach preserves spectral, spatial and temporal structures and extracts features which are less sensitive to variations along each dimension. Our results demonstrate cognitive memory load prediction across four different levels with an overall accuracy of 92.5% during the memory task execution and reduce classification error to 7.61% in comparison to other state-of-art techniques.

High Efficiency Video Coding (HEVC), which is the latest video coding standard currently, achieves up to 50% bit rate reduction compared to previous H.264/AVC standard. While performing the block based video coding, these lossy compression techniques produce various artifacts like blurring, distortion, ringing, and contouring effects on output frames, especially at low bit rates. To reduce those compression artifacts HEVC adopted two post processing filtering technique namely de-blocking filter (DBF) and sample adaptive offset (SAO) on the decoder side. While DBF applies to samples located at block boundaries, SAO nonlinear operation applies adaptively to samples satisfying the gradient based conditions through a lookup table. Again SAO filter corrects the quantization errors by sending edge offset values to decoders. This operation consumes extra signaling bit and becomes an overhead to network. In this paper, we proposed a Convolutional Neural Network (CNN) based architecture for SAO in-loop filtering operation without modifying anything on encoding process. Our experimental results show that our proposed model outperformed previous state-of-the-art models in terms of BD-PSNR (0.408 dB) and BD-BR (3.44%), measured on a widely available standard video sequences.

Dual-fisheye lens cameras are becoming popular for 360-degree video capture, especially for User-generated content (UGC), since they are affordable and portable. Images generated by the dual-fisheye cameras have limited overlap and hence require non-conventional stitching techniques to produce high-quality 360×180-degree panoramas. This paper introduces a novel method to align these images using interpolation grids based on rigid moving least squares. Furthermore, jitter is the critical issue arising when one applies the image-based stitching algorithms to video. It stems from the unconstrained movement of stitching boundary from one frame to another. Therefore, we also propose a new algorithm to maintain the temporal coherence of stitching boundary to provide jitter-free 360-degree videos. Results show that the method proposed in this paper can produce higher quality stitched images and videos than prior work.

Searching for an efficient summarization of multi-channel electroencephalogram (EEG) behavior is a challenging signal analysis problem. Recently, parallel factor analysis (PARAFAC) is reported as an efficient tool for extracting features of multi-channel EEG by simultaneously employing space-time-frequency knowledge, i.e. decomposing multi-channel EEG signal into a linear combination of its space-time-frequency feature. However, this decomposition scheme suffers from expensive computational load when applied to either long term or high number of channels EEG signals. In this paper, a reduced computational complexity space-time-frequency model for multi-channel EEG signal is proposed by dividing selected content into segments yielding additional segment signatures. By carefully selecting the number of segments, features extracted from the proposed model are comparable with those from the conventional space-time-frequency model while the time used in computation is reduced by more than 50%. Simulation results show that the proposed model can efficiently extract eye blink artifact from background EEG. Furthermore, classification accuracy when employing the proposed model to brain computer interface (BCI) application is also comparable with the conventional model.

This paper presents a method for losslessly compressing multi-channel electroencephalogram signals. The Karhunen-Loeve transform is used to exploit the inter-correlation among the EEG channels. The transform is approximated using lifting scheme which results in a reversible realization under finite precision processing. An integer time-frequency transform is applied to further minimize the temporal redundancy

Multimedia authentication techniques are required to prove the validity of legal multimedia content and establish the identity of the content creator. Digital signatures are one way of authenticating multimedia content. Typically digital signatures use cryptographic techniques to ensure the integrity of the multimedia bitstream. This paper proposes a hard video authentication and sender verification scheme for video sequences compressed using H.264/AVC Main Profile by using digital signatures and cryptographic hash. Features from the transform domain are used as the authentication data for a macroblock. The algorithm can also detect the cause of authentication failure and point out the location of the tampered frames in case of frame tampering. Results demonstrate that the proposed scheme is highly robust to temporal and spatial manipulations.

In this paper, lossless audio coding using the integer modified discrete cosine transform (IntMDCT) is discussed. The IntMDCT is constructed as an integer approximation of the MDCT using the lifting scheme and is reversible. The rounding error shape of the IntMDCT is derived. When the spectral energy of the input audio signal is concentrated at the low frequencies, the rounding error spectrum limits the lossless coding performance. A method for shaping the rounding error in the transform domain is presented. This rounding error shaping scheme manipulates the error so that it is below the spectral envelope of the signal at the high frequencies in order to improve the lossless coding performance for the signal. Examples of an error shaping filter design are presented and verified by simulations. An IntMDCT-based lossless coding implementation is carried out to illustrate the use of the error shaping filters

The integer modified discrete cosine transform (IntMDCT), an integer approximation of the MDCT, is a reversible transform realized by the lifting scheme and thus is a useful transform for lossless audio coding. Because of the integer approximation, however, the approximation error appears as a "noise floor" in the transform domain and limits the lossless coding efficiency. In this paper, a theoretical analysis of the approximation error of the IntMDCT is discussed. The result is then used to design a simple test filter applied to each rounding operation of the IntMDCT in such a way that the error spectrum is shaped towards the low frequencies. As a result, especially when the spectral energy of an input signal is concentrated in the low frequency domain, the lossless coding efficiency is improved.

The modified discrete cosine transform (MDCT) is employed in subband/transform coding schemes as the analysis/synthesis filter bank based on time domain aliasing cancellation (TDAC). The most efficient implementation of the forward and inverse MDCT computation for layer III in MPEG-1 and MPEG-2 international audio coding standards is proposed. It is based on a new fast algorithm for the forward and inverse MDCT computation in the oddly stacked system. The complete signal flow graphs for the implementation of MDCT and inverse MDCT in layer III are also provided.

In the above-named aerticle [ibid., vol. 10, pp. -51, Feb. 2001], errors in the expressions of the forward and inverse 9-point DCT/DST modules (p. 51) have been found. Corrected versions of those expressions are presented here.

This paper describes a new motion estimation algorithm for block based video compression. Unlike other fast algorithms, the proposed method works efficiently with the adaptive size of data depending on the local information. Motion vector estimated by this mechanism provides a high accuracy close to that of a full search. However, fewer search points are employed in the process leading to a lower complexity. Although the number of searches is greater than that of hierarchical or other fast algorithms, it is less vulnerable to the local minima and also yields an efficient tool for the existing compression standards since it only computes on a fixed block size. The simulation results show the closeness in performance between the new method and the full search BMA.

The progressive image transmission (PIT) allows an approximate image to be built up quickly with details to be transmitted progressively through several passes over the image. In this paper, we propose an efficient PIT scheme in which two-channel conjugate classified vector quantization (TCCVQ) is applied to the subvectors formed from the classified wavelet transform blocks. The use of these two techniques allows efficient bit-rate reduction and reduces coding artifacts (i.e., blocking effects and distorted edges) at low bit rates. The adaptive classification technique is utilized to classify an image into four perceptually distinct categories. Simulation results show that the first stage image already provides a useful approximation and reconstructed images, at the intermediate levels, preserve fine and pleasant qualities based on both subjective and mean square error criteria compared to other schemes.

The discrete wavelet transform (DWT) is incorporated into the JPEG baseline system for image coding. The discrete cosine transform (DCT) is replaced by an association of two-channel filter banks connected hierarchically. The JPEG block-scanning and quantization schemes are adopted while we use JPEG's entropy coder. The changes in scanning can be incorporated into the transform block in such a way that the only part that needs to be changed in a JPEG framework is to replace the DCT by the DWT. Objective results and reconstructed images are presented demonstrating that the proposed coder outperforms JPEG and approaches the performance of more sophisticated and complex wavelet coders. However, it does not require full-image buffering nor imposes a large complexity increase.

A new technique to compress image data is introduced. Based on hierarchical properties of the tree structure, appropriate features can be drawn from specific region resulting in variable blocksize partitioning. To simplify the operation, the proposed scheme applies a scaling process to the derived feature. This scaling is similar to normalization of input vector to a unified dimension thereby a single codebook is used. This arrangement reduces complexity of the vector quantization (VQ) process dramatically. As a single pass algorithm, this VQ which uses image data in 3 regular sizes requires a minimal overhead. The simulation results show that this method not only decreases the search time but improves the quality of reconstructed images at low bit rates as well.

This paper describes a progressive image transmission (PIT) scheme using a variable block size coding technique in conjunction with a variety of quantization schemes in the transform domain. The proposed scheme uses a region growing technique to partition the images so that regions of different sizes can be addressed using a small amount of side information. This segmentation divides the image into five different regions that vary in size based on the details within the image. High detail blocks are classified into four different categories based on the energy distribution followed by vector quantization (VQ), and low-detail blocks are encoded with scalar quantization (SQ). Progressive refinement is achieved by proper masking of the information in the transform domain. Simulation results show that the reconstructed images preserve fine and pleasant qualities based on both subjective and mean square error criteria. Also, the receiver reconstructs more details in each stage so that the observer can recognize the image quickly.

The use of a paraunitary filter bank for image processing requires a special treatment at image boundaries to ensure perfect reconstruction and orthogonality of these regions. Using time-varying boundary filter banks, we will discuss a procedure that explores all degrees of freedom of the border filters in a method essentially independent of signal extensions, allowing us to design optimal boundary filter banks, while maintaining fast implementation algorithms.

A structure for implementing lapped transforms with time-varying block sizes is discussed. It allows full orthogonality in the transitions based on a factorization of the transfer matrix into orthogonal factors. Such an approach can be viewed as a sequence of stages with variable-block-size transforms intermediated by sample-shuffling (delay) stages. Details for a first order system are given and a design example is presented.

A new coding scheme for image compression using classified two-channel conjugate vector quantization (TCCVQ) of the wavelet coefficients is proposed. This scheme exploits residual correlation among different layers of the discrete wavelet transform (DWT) domain and thereby improves the encoding efficiency by taking advantage of the DWT and TCCVQ, which requires less computational complexity and less storage (memory). In this scheme, DWT coefficients are rearranged to form the small blocks, which are composed of the corresponding coefficients from all subbands. The block matrices, then, are classified and further divided into subvectors depending on the DWT coefficient statistics as this allows efficient distribution of bits. Simulation results show that the reconstructed images preserve fine and pleasant qualities based on both subjective and mean square error criteria at a bit rate of 0.3 bit/pel (bpp).>

Classified transform coding of images using vector quantization (VQ) has proved to be an efficient technique. Transform VQ combines the energy compaction properties of transform coding and the superior performance of VQ. Classification improves the reconstructed image quality considerably because of adaptive bit allocation. A classified transform VQ technique using the lapped orthogonal transform (LOT) is presented. Image blocks are transformed using the LOT and are classified into four classes based on their structural properties. These are further divided adaptively into subvectors depending on the LOT coefficient statistics as this allows efficient distribution of bits. These subvectors are then vector quantized. Simulation results indicate subjectively improved images with LOT/VQ as compared to DCT/VQ.>

A modulated lapped transform with extended overlap (ELT) is investigated in image coding with the objective of verifying its potential to replace the discrete cosine transform (DCT) in specific applications. Some of the criteria utilized for the performance comparison are reconstructed image quality (both objective and subjective), reduction of blocking artifacts, robustness against transmission errors, and filtering (for scalability). Also, a fast implementation algorithm for finite-length-signals using symmetric extensions is developed specially for the ELT with overlap factor 2 (ELT-2). This comparison shows that ELT-2 is superior to both DCT and the lapped orthogonal transform (LOT).

In this paper, we propose a new coding scheme for image compression using classified two-channel conjugate vector quantization (TC-CVQ) of the wavelet coefficients. This scheme exploits residual correlation among different layers of the discrete wavelet transform (DWT) domain and improves the encoding efficiency. In addition, two-channel conjugate VQ requires less computational complexity and less storage (memory). Simulation results show that the reconstructed images preserve fine and pleasant qualities based on both subjective and mean square error criteria at a bit rate of 0.3 bit/pel(bpp).>

Periodic or symmetric extensions are commonly used for processing images and other finite-length signals with a paraunitary filter bank (PUFB). Unlike infinite-length signals, PUFBs applied to finite-length signals will not necessarily lead to an orthogonal system. The authors show that for symmetric extensions, orthogonality is only possible for special PUFBs based on linear-phase filters. They also discuss implementation issues.>

The general factorization of a linear-phase paraunitary filter bank (LPPUFB) is revisited and we introduce a class of lapped orthogonal transforms with extended overlap (GenLOT). In this formulation, the discrete cosine transform (DCT) is the order-1 GenLOT, the lapped orthogonal transform is the order-2 GenLOT, and so on, for any filter length which is an integer multiple of the block size. All GenLOTs are based on the DCT and have fast implementation algorithms. The degrees of freedom in the design of GenLOTs are described and design examples are presented along with some practical applications.>

Progressive image transmission (PIT) is widely used in many applications, since it generates the successively improved reconstructions of an image. In spatial domain PIT systems, perfectly reconstructed images can be obtained at the final stage. However the intermediate images are not good and there is no data compression. In this paper, the authors present a new simple spatial domain progressive image transmission using modified Kohonen self-organizing feature map algorithm, which is called Kohonen vector quantizer (KVQ). To alleviate edge distortion a classification technique is applied to KVQ. Computer simulation results show that very good intermediate images can be obtained at reasonable bit rates using the PIT scheme introduced. >

An adaptive image coding technique-two-channel conjugate classified discrete cosine transform/vector quantization (TCCCDCT/VQ)-is proposed to efficiently exploit correlation in large image blocks by taking advantage of the discrete cosine transform and vector quantization. In the transform domain, a classified discrete cosine transform/vector quantization (CDCT/VQ) scheme is proposed and TCCCDCT/VQ is developed based on the CDCT/VQ scheme. These two techniques were applied to encode test images at about 0.51 b/pixel and 0.73 b/pixel. The performances of both techniques over a noisy channel have been also tested in the transform domain. The performances of both adaptive VQ techniques are perceptually very similar for the noise-free channel case. However, when channel error is injected for the same bit rate, the TCCCDCT/VQ results in less visible distortion than the CDCT/VQ, which is based on ordinary VQ.>

Circular convolution-multiplication relationships for the discrete cosine transform (DCT) that are similar to those for the discrete Fourier transform (DFT) are developed. The relations are valid if the filter frequency response is real and even. Two fairly simple relations are developed. The multiplication of the DCT of signal sequence and the DFT of filter sequence results in circular convolution of the folded signal sequence and the filter sequence. Thus, it can be used to filter an image in the frequency domain as an approximation of circular convolution in the spatial domain.>

A progressive image transmission scheme which combines transform coding with the human visual system (HVS) model is developed. The adaptive transform coding of W.H. Chen and C.H. Smith (1977) is utilized to classify an image into four equally populated subblocks based on their AC energies. The modulation transfer function (MTF) of the HVS model is obtained experimentally, based on processing a number of test images. A simplified technique for incorporating the MTF into the discrete cosine transform (DCT) domain is utilized. In the hierarchical image buildup, the image is first reconstructed from the DC coefficients of all subblocks. Further transmission hierarchy of transform coefficients and consequent image buildup are dependent on their HVS weighted variances. The HVS weighted reconstructed images are compared to the ones without any weighting at several stages. The HVS weighted progressive image transmission results in perceptually higher quality images compared to the unweighted scheme.>

It is shown that the N-point DFT (discrete Fourier transform) of a real sequence can be implemented via the real (cos DFT) and imaginary (sin DFT) components. The N-point cos DFT in turn can be developed from the N/2-point cos DFT and N/4-point discrete sine transform (DST). Similarly the N-point sin DFT can be developed from N/2-point sin DFT and N-point DST. Using this approach, an efficient algorithm (involving real arithmetic only) for an N-point DFT is developed. The basic DST algorithm has an orderly architecture and recursive structure. Because of its regularity and symmetry, the algorithm is conducive to simple hardware implementation.>

A codec for videoconferencing purposes [8]-[12], [31] is proposed based on the one-at-a-time search (OTS) motion compensation algorithm [1], [30], [31]. The coder is implemented in an interframe hybrid mode using theC-matrix transform (CMT) [13]-[15]. The motion estimation algorithm employed is simple and reduces temporal redundancy, while the CMT reduces spatial redundancy in the transmitted prediction errors. The operation of the codec is presented. Simulation results based on three different scenes with varying levels of motion are presented. The coder operates in a feedback mode.

This paper presents a simple and effective algorithm for an adaptive multifrequency receiver that can be used for several types of multifrequency signals. This algorithm uses the ability of frequency detection of signal processing using extreme and zero-crossing points in the multifrequency signals and an adaptive second-order notch filter.

In an earlier paper, an extension of the pel recursive techniques of Netravali and Robbins [2] and Cafforio and Rocca [3] was introduced. Here a method is provided to realize the algorithm in hardware, with some approximations. The prediction error distribution allows the use of quantized variables to a lookup table of reasonable size. The algorithm is then incorporated into a simple multimode coder capable of 1.5 bits/pel on the sequence examined. The coder incorporates a spot filter, quantizer, block run length coding, and variable word length coding and subsampling. Simulation results are presented, including bit rate, buffer status, and mode control analysis.

Decimation-In-Frequency (DIF) algorithms for a family of discrete cosine and sine transforms (DCT) and (DST) are systematically developed, based on a radix-2 factorization of the transformation matrices. The results indicate these to be viable alternatives to existing algorithms for the calculation of these discrete transforms. The algorithms are all recursive in nature, making for a modular structure in possible hardware implementations.

Interframe motion estimation of subblocks based on improved search techniques is developed. These techniques are based on minimizing the mean difference between the subblock in question in the present frame and the displaced subblock in the previous frame. The performance of the motion compensated prediction developed here is investigated for various block sizes and is compared to other techniques.

A computationally simpler and effective method is proposed for estimating motion in a video sequence. The paper outlines a search technique based on conjugate directions [3], [4] and another simpler technique called the one-at-a-time search [3]. Based on the comparison of the two methods, the latter technique is adopted as the basis for further research. The adopted technique is compared with brute force search, existing 2-D logarithmic search [1], and a modified version of it [2], for motion compensated prediction [5].

An investigation of coding the NTSC color TV signal in the component form is carried out. C-matrix transform (CMT) and the hybrid (CMT/DPCM) coding are simulated on an intrafield basis. These techniques are found to be closely comparable to DCT and the corresponding hybrid coding techniques [15, 16]. CMT, which is an integer approximation to the DCT, is expected to yield almost the same processed picture quality as the DCT with less hard-ware.

Component coding of the NTSC color TV signal is investigated. This coding involves digital demodulation of the composite signal sampled at three times the color subcarrier frequency, the implementation of the compression algorithms on the subsampled component signal, and digital reconstruction of the processed NTSC color signal. The comb filter, bandpass filter, and Hilbert transformer are used for the demodulation of the luminance and theIandQchrominance signals. The reconstructed components at the receiver are interpolated and modulated to obtain the composite signal. Different combinations of comb filters, bandpass filters and Hilbert transformers are used to investigate their effect on compositecomponent separation and reconstruction. Because of their reduced bandwidths, the chrominance signals are subsampled both horizontally and vertically. Several intrafield and intraline predictors are simulated. Of these, three predictors with small variances of the prediction error are combined with 4 and 3 bit Max quantizers for further processing and transmission in a TDM format. The data compression algorithms have been applied to color test pictures and their effectiveness is compared on the basis of quantitative criteria. The bandwidth reduction technique results in digital transmission of a single color TV signal at 32-43 Mbits/s.

A pel-recursive motion estimation technique for television coding was introduced by Netravali and Robbins [1]. This method basically involves computing a motion displacement and then separating the pels into predictable and unpredictable segments. The addresses required to identify these segments and thus enable the motion estimation algorithm are transmitted along with pel error data. The original algorithms are slow to converge, i.e., many iterations are required to obtain an accurate displacement estimate. This research introduces extensions to the basic algorithm of [1] and offers two significant improvements. First, convergence speed is improved substantially, which means that the algorithms can better tolerate motion changes and diverse motion within the picture. Secondly, explicit address information is not required, as it is contained implicitly in the motion compensation algorithm. For the sequences examined, this method proved superior to that of explicitly transmitting the address data. This algorithm has much better convergence rates and has prediction rates better than the original.

An investigation of coding the NTSC color TV signal in the component form is carried out.C-matrix transform (CMT) and the hybrid (CMT/DPCM) coding are simulated on an intrafield basis. The techniques are found to be closely comparable to the discrete cosine transform (DCT) and the corresponding hybrid coding techniques. CMT, which is an integer approximation to the DCT, is expected to yield almost the same processed picture quality as the DCT with less hardware.

Two types of efficient algorithms for fast implementation of the 2-D discrete cosine transform (2-D DCT) are developed. One involves recursive structure which implies that the algorithm for (M/2 X N/2) block be extended to (M X N/2) (M/2 X M) and (M X N) blocks (M and N are integer powers of two). The second algorithm is nonrecursive and therefore it has to be tailored for each block size. Both algorithms involve real arithmetic and they reduce the number of multiplications significantly compared to the fast algorithm developed by Chen et al. [8], while the number of additions remain unchanged.

This paper describes two different schemes of DCT/ DPCM processing of digital NTSC composite video signal. The first scheme (line processing) is based on applying the discrete cosine transform (DCT) along each horizontal line and then implementing the differential pulse code modulation (DPCM) in the vertical direction on the semitransformed image. The second scheme (block processing) involves DCT of (4 × 4) subblocks followed by adaptive DPCM to reduce intersubblock correlation. Based on the statistics of the prediction error, variable bit quantizers optimized for minimizing the mean-square quantization error are developed. These techniques lead to reduced bit rates for transmitting the color video at broadcast standards. Both original and processed color images in composite form are displayed for subjective evaluation. The effects of channel error on block processing are also investigated.

Hybrid coding of color television images at broadcast standards is investigated. This involves two-dimensional discrete cosine transform (2-D DCT) of each field, followed by the differential pulse code modulation (DPCM) between successive fields. Two 22frame sequences of "Water Skier" and "Wheel of Fortune" in component form, i.e., luminanceYand chrominanceIandQ, were utilized as the database. A statistical study of the prediction error in the 2-D DCT domain is carried out. Three different algorithms for the 2-D DCT system are simulated and analyzed. In the first algorithm, optimum (nonuniform) quantizers are used in DPCM loops followed by fixed-wordlength coders. Uniform quantizers along with variablewordlength coders are implemented in the second system. The performances of different deterministic coders are investigated and compared with Huffman coders. The third scheme is an adaptive system. In this system each 8 × 8 block is divided into four subblocks. The activity of each subblock is monitored and when it exceeds some threshold, the subblock is considered to be spatially active. More bits are assigned to active subblocks and the ranges of corresponding quantizers are expanded. The prediction error of the dc coefficient is monitored to determine the temporal activity of a block. For a temporally active block, the number of bits assigned to the two lower frequency subblocks is increased. Performance of these three systems for unmatched statistics and in the case of a scene change are studied. Mean square error (MSE) between the original and reconstructed images, bit rate, entropy, essential maximum, and other parameters are utilized as the performance criteria. Also, a subjective evaluation of the processed images is carried out. It is shown that the interfield adaptive hybrid coding of color TV signals in component form results in significant savings in bit rates for transmission over a digital link.

New adaptive differential pulse code modulation (ADPCM) coders with adaptive prediction are proposed and compared with existing nonadaptive DPCM coders, for processing composite National Television System Commission (NTSC) television signals. Comparisons are based on quantative criteria as well as subjective evaluation of the processed still frames. The performance of the proposed predictors is shown to be independent of well-designed quantizers and better than existing predictors in such critical regions of the pictures as edges and contours.

A sparse-matrix factorization is developed for the discrete sine transform (DST). This factorization has a recursive structure and leads directly to an efficient algorithm for implementing the DST, a feature most desirable and very similar ot that of the DCT. This algorithm requires fewer arithmetic operations compared to that for the discrete cosine transform (DCT).

The concept of energy packing efficiency (EPE) of the Walsh-Hadamard transform (WHT) first proposed by Kitajima [1], is extended to other discrete orthogonal transforms. The concept as a criterion for evaluating the transforms is discussed. It is shown that the EPE is invariant for the generalized transforms as long as the ordering is the same.

Transform-DPCM (hybrid) techniques are applied to image data processing. For achieving bandwidth reduction, sample selection (threshold or variance) and variable bit allocation are adopted. The hybrid process is compared with the two-dimensional transform method in terms of bit rate, mean-square error, and computational complexity.

A tutorial-review paper on discrete orthogonal transforms and their applications in digital signal and image (both monochrome and color) processing is presented. Various transforms such as discrete Fourier, discrete cosine, Walsh-Hadamard, slant, Haar, discrete linear basis, Hadamard-Haar, rapid, lower triangular, generalized Haar, slant Haar and Karhunen-Loêve are defined and developed. Pertinent properties of these transforms such as power spectra, cyclic and dyadic convolution and correlation are outlined. Efficient algorithms for fast implementation of these transforms based on matrix partitioning or matrix factoring are presented. The application of these transforms in speech and image processing, spectral analysis, digital filtering (linear, nonlinear, optimal and suboptimal), nonlinear systems analysis, spectrography, digital holography, industrial testing, spectrometric imaging, feature selection, and patter recognition is presented. The utility and effectiveness of these transforms are evaluated in terms of some standard performance criteria such as computational complexity, variance distribution, mean-square error, correlated rms error, rate distortion, data compression, classification error, and digital hardware realization.

With the aid of statistical detection theory, the continuous optimum Bayes recognition scheme for machine characters is developed using a sufficient statistic approach. This result is then extended to the discrete case and the associated problems such as the sampling effects are examined. Using the discrete optimum recognition model, design parameters are then developed. Among these are the critical sampling matrix which provides a lower bound for the sampling rates and the rate matrix which provides information on the classification error. Algorithms such as the two-dimensional fast Fourier transform are then employed to calculate these discrete optimum model design parameters. Based on this theoretical background a machine print recognition problem is presented. The design parameters are computed and the discrete optimum system is simulated on the digital computer. Finally some actual machine print data is recognized and the results are analyzed.

A hybrid version of the Haar and Walsh-Hadamard transforms (HT and WHT) called Hadamard-Haar transform (HHT),is defined and developed. Efficient algorithms for fast computation of the (HHT), and its inverse are developed. (HHT)r is applied to digital signal and image processing and its utility and effectiveness are compared with other discrete transforms on the basis of some standard performance criteria.

A discrete cosine transform (DCT) is defined and an algorithm to compute it using the fast Fourier transform is developed. It is shown that the discrete cosine transform can be used in the area of digital processing for the purposes of pattern recognition and Wiener filtering. Its performance is compared with that of a class of orthogonal transforms and is found to compare closely to that of the Karhunen-Loève transform, which is known to be optimal. The performances of the Karhunen-Loève and discrete cosine transforms are also found to compare closely with respect to the rate-distortion criterion.

Cyclic and dyadic shifts of a periodic sequence are illustrated on the H diagram. Fast Walsh-Hadamard transform of the shifted (both cyclic and dyadic) sequence is represented graphically on the H diagram. The shift-invariant properties of the power spectrum are derived from these operations.

Using elementary matrix partitioning techniques, a fast algorithm for computing the complex BIFORE transform is developed.