An End-to-End Deep Learning Image Compression Framework Based on Semantic Analysis

Lossy image compression can reduce the bandwidth required for image transmission in a network and the storage space of a device, which is of great value in improving network efficiency. With the rapid development of deep learning theory, neural networks have achieved great success in image processing. In this paper, inspired by the diverse extent of attention in human eyes to each region of the image, we propose an image compression framework based on semantic analysis, which creatively combines the application of deep learning in the field of image classification and image compression. We first use a convolutional neural network (CNN) to semantically analyze the image, obtain the semantic importance map, and propose a compression bit allocation algorithm to allow the recurrent neural network (RNN)-based compression network to hierarchically compress the image according to the semantic importance map. Experimental results validate that the proposed compression framework has better visual quality compared with other methods at the same compression ratio.

Two-band hybrid FIR-IIR filters for image compression

Two-band analysis-synthesis filters or wavelet filters are used pervasively for compressing natural images. Both FIR and IIR filters have been studied in this context, the former being the most popular. In this paper, we examine the compression performance of these two-band filters in a dyadic wavelet decomposition and attempt to isolate features that contribute most directly to the performance gain. Then, employing the general exact reconstruction condition, hybrid FIR-IIR analysis-synthesis filters are designed to maximize compression performance for natural images. Experimental results are presented that compare performance with the popular biorthogonal filters in terms of peak SNR, subjective quality, and computational complexity.

A video coding scheme based on joint spatiotemporal and adaptive prediction

We propose a video coding scheme that departs from traditional Motion Estimation/DCT frameworks and instead uses Karhunen-Loeve Transform (KLT)/Joint Spatiotemporal Prediction framework. In particular, a novel approach that performs joint spatial and temporal prediction simultaneously is introduced. It bypasses the complex H.26x interframe techniques and it is less computationally intensive. Because of the advantage of the effective joint prediction and the image-dependent color space transformation (KLT), the proposed approach is demonstrated experimentally to consistently lead to improved video quality, and in many cases to better compression rates and improved computational speed.

Adaptive wavelet packet basis selection for zerotree image coding

Image coding methods based on adaptive wavelet transforms and those employing zerotree quantization have been shown to be successful. We present a general zerotree structure for an arbitrary wavelet packet geometry in an image coding framework. A fast basis selection algorithm is developed; it uses a Markov chain based cost estimate of encoding the image using this structure. As a result, our adaptive wavelet zerotree image coder has a relatively low computational complexity, performs comparably to state-of-the-art image coders, and is capable of progressively encoding images.

Image subband coding using fuzzy inference and adaptive quantization

Wavelet image decomposition generates a hierarchical data structure to represent an image. Recently, a new class of image compression algorithms has been developed for exploiting dependencies between the hierarchical wavelet coefficients using zerotrees. This paper deals with a fuzzy inference filter for image entropy coding by choosing significant coefficients and zerotree roots in the higher frequency wavelet subbands. Moreover, an adaptive quantization is proposed to improve the coding performance. Evaluating with the standard images, the proposed approaches are comparable or superior to most state-of-the-art coders. Based on the fuzzy energy judgment, the proposed approaches can achieve an excellent performance on the combination applications of image compression and watermarking.

Cascaded differential and wavelet compression of chromosome images

This paper proposes a new method for chromosome image compression based on an important characteristic of these images: the regions of interest (ROIs) to cytogeneticists for evaluation and diagnosis are well determined and segmented. Such information is utilized to advantage in our compression algorithm, which combines lossless compression of chromosome ROIs with lossy-to-lossless coding of the remaining image parts. This is accomplished by first performing a differential operation on chromosome ROIs for decorrelation, followed by critically sampled integer wavelet transforms on these regions and the remaining image parts. The well-known set partitioning in hierarchical trees (SPIHT) (Said and Perlman, 1996) algorithm is modified to generate separate embedded bit streams for both chromosome ROIs and the rest of the image that allow continuous lossy-to-lossless compression of both (although lossless compression of the former is commonly used in practice). Experiments on two sets of sample chromosome spread and karyotype images indicate that the proposed approach significantly outperforms current compression techniques used in commercial karyotyping systems and JPEG-2000 compression, which does not provide the desirable support for lossless compression of arbitrary ROIs.

Wavelet-based space-frequency compression of ultrasound images

This paper describes the compression of grayscale medical ultrasound images using a recent compression technique, i.e., space-frequency segmentation (SFS). This method finds the rate-distortion optimal representation of an image from a large set of possible space-frequency partitions and quantizer combinations and is especially effective when the images to code are statistically inhomogeneous, which is the case for medical ultrasound images. We implemented a compression application based on this method and tested the algorithm on representative ultrasound images. The result is an effective technique that performs better than a leading wavelet-transform coding algorithm, i.e., set partitioning in hierarchical trees (SPIHT), using standard objective distortion measures. To determine the subjective qualitative performance, an expert viewer study was run by presenting ultrasound radiologists with images compressed using both SFS and SPIHT. The results confirmed the objective performance rankings. Finally, the performance sensitivity of the space-frequency codec is shown with respect to several parameters, and the characteristic space-frequency partitions found for ultrasound images are discussed.

Rate-distortion-constrained subband video coding

This paper introduces a subband video coding algorithm for operation over a continuum of rates from very low to very high. The key elements of the system are statistical rate-distortion-constrained motion estimation and compensation, multistage residual quantization, high order statistical modeling, and arithmetic coding. The method is unique in that it provides an improved mechanism for dynamic spatial and temporal coding. Motion vectors are determined in a nontraditional way, using a rate-distortion cost criterion. This results in a smoother and more consistent motion field, relative to that produced by conventional block matching algorithms. Control over the system computational complexity and performance may be exercised easily.

Optimal biorthogonal wavelet decomposition of wire-frame meshes using box splines, and its application to the hierarchical coding of 3-D surfaces

Optimal mechanisms are determined for the hierarchical decomposition of wire-frame surfaces generated by box splines. A family of box splines with compact support, suitable for the approximation of wire-frames is first defined, generated by arbitrary sampling matrices with integer eigenvalues. For each such box spline, the optimal positioning of the wire-frame nodes is determined for each level of the hierarchical wire-frame decomposition. Criterion of optimality is the minimization of the variance of the error difference between the original surface and its representation at each resolution level. This is needed so as to ensure that the wire mesh produces at each resolution as close a replica of the original surface as possible. Several such combinations of box spline generated meshes and the corresponding optimal node lattice sequences are examined in detail with a view to practical application. Their specific application to the hierarchical coding of three-dimensional (3-D) wire meshes is experimentally evaluated.

A progressively predictive image pyramid for efficient lossless coding

A low entropy pyramidal image data structure suited for lossless coding and progressive transmission is proposed in this work. The new coder, called the progressively predictive pyramid (PPP) is based on the well-known Laplacian pyramid. By introducing inter-resolution predictors into the original Laplacian pyramid, we show that the entropy level in the original pyramid can be reduced significantly. To take full advantage of progressive transmission, a scheme is introduced to create the predictor adaptively, thus eliminating the need to transmit the predictor and reducing the coding overheads. A method for designing the predictor is presented. Numerical results show that PPP is superior to traditional approaches to pyramid generation in the sense that the pyramids generated by PPP always have significantly lower entropy values.

Subband domain coding of binary textual images for document archiving

In this work, a subband domain textual image compression method is developed. The document image is first decomposed into subimages using binary subband decompositions. Next, the character locations in the subbands and the symbol library consisting of the character images are encoded. The method is suitable for keyword search in the compressed data. It is observed that very high compression ratios are obtained with this method. Simulation studies are presented.

Fast reconstruction of subband-decomposed progressively transmitted signals

We propose a fast reconstruction method for a subband-decomposed, progressive signal coding system. We show that unlike the conventional approach which requires a fixed computational complexity, the computational complexity of the proposed approach is proportional to the number of refined coefficients at each level of progression. Therefore, unrefined coefficients do not add to the computational complexity of the proposed scheme. It is shown, through specific examples, that the proposed approach can lead to significant reductions in reconstruction complexity. Furthermore, the proposed approach provides the capability for an online updating of the reconstructed image based on receiving the refinement of each coefficient.

Image compression via joint statistical characterization in the wavelet domain

We develop a probability model for natural images, based on empirical observation of their statistics in the wavelet transform domain. Pairs of wavelet coefficients, corresponding to basis functions at adjacent spatial locations, orientations, and scales, are found to be non-Gaussian in both their marginal and joint statistical properties. Specifically, their marginals are heavy-tailed, and although they are typically decorrelated, their magnitudes are highly correlated. We propose a Markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties, and show that it accounts for the statistics of a wide variety of images including photographic images, graphical images, and medical images. In order to directly demonstrate the power of the model, we construct an image coder called EPWIC (embedded predictive wavelet image coder), in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model. Bitplanes are ordered using a greedy algorithm that considers the MSE reduction per encoded bit. The decoder uses the statistical model to predict coefficient values based on the bits it has received. Despite the simplicity of the model, the rate-distortion performance of the coder is roughly comparable to the best image coders in the literature.

Image coding based on a morphological representation of wavelet data

In this paper, an experimental study of the statistical properties of wavelet coefficients of image data is presented, as well as the design of two different morphology-based image coding algorithms that make use of these statistics. A salient feature of the proposed methods is that, by a simple change of quantizers, the same basic algorithm yields high performance embedded or fixed rate coders. Another important feature is that the shape information of morphological sets used in this coder is encoded implicitly by the values of wavelet coefficients, thus avoiding the use of explicit and rate expensive shape descriptors. These proposed algorithms, while achieving nearly the same objective performance of state-of-the-art zerotree based methods, are able to produce reconstructions of a somewhat superior perceptual quality, due to a property of joint compression and noise reduction they exhibit.

Image subband coding using context-based classification and adaptive quantization

Adaptive compression methods have been a key component of many proposed subband (or wavelet) image coding techniques. This paper deals with a particular type of adaptive subband image coding where we focus on the image coder's ability to adjust itself "on the fly" to the spatially varying statistical nature of image contents. This backward adaptation is distinguished from more frequently used forward adaptation in that forward adaptation selects the best operating parameters from a predesigned set and thus uses considerable amount of side information in order for the encoder and the decoder to operate with the same parameters. Specifically, we present backward adaptive quantization using a new context-based classification technique which classifies each subband coefficient based on the surrounding quantized coefficients. We couple this classification with online parametric adaptation of the quantizer applied to each class. A simple uniform threshold quantizer is employed as the baseline quantizer for which adaptation is achieved. Our subband image coder based on the proposed adaptive classification quantization idea exhibits excellent rate-distortion performance, in particular at very low rates. For popular test images, it is comparable or superior to most of the state-of-the-art coders in the literature.

Significance-linked connected component analysis for wavelet image coding

Recent success in wavelet image coding is mainly attributed to a recognition of the importance of data organization and representation. There have been several very competitive wavelet coders developed, namely, Shapiro's (1993) embedded zerotree wavelets (EZW), Servetto et al.'s (1995) morphological representation of wavelet data (MRWD), and Said and Pearlman's (see IEEE Trans. Circuits Syst. Video Technol., vol.6, p.245-50, 1996) set partitioning in hierarchical trees (SPIHT). We develop a novel wavelet image coder called significance-linked connected component analysis (SLCCA) of wavelet coefficients that extends MRWD by exploiting both within-subband clustering of significant coefficients and cross-subband dependency in significant fields. Extensive computer experiments on both natural and texture images show convincingly that the proposed SLCCA outperforms EZW, MRWD, and SPIHT. For example, for the Barbara image, at 0.25 b/pixel, SLCCA outperforms EZW, MRWD, and SPIHT by 1.41 dB, 0.32 dB, and 0.60 dB in PSNR, respectively. It is also observed that SLCCA works extremely well for images with a large portion of texture. For eight typical 256x256 grayscale texture images compressed at 0.40 b/pixel, SLCCA outperforms SPIHT by 0.16 dB-0.63 dB in PSNR. This performance is achieved without using any optimal bit allocation procedure. Thus both the encoding and decoding procedures are fast.

Operational rate-distortion performance for joint source and channel coding of images

This paper describes a methodology for evaluating the operational rate-distortion behavior of combined source and channel coding schemes with particular application to images. In particular, we demonstrate use of the operational rate-distortion function to obtain the optimum tradeoff between source coding accuracy and channel error protection under the constraint of a fixed transmission bandwidth for the investigated transmission schemes. Furthermore, we develop information-theoretic bounds on performance for specific source and channel coding systems and demonstrate that our combined source-channel coding methodology applied to different schemes results in operational rate-distortion performance which closely approach these theoretical limits. We concentrate specifically on a wavelet-based subband source coding scheme and the use of binary rate-compatible punctured convolutional (RCPC) codes for transmission over the additive white Gaussian noise (AWGN) channel. Explicit results for real-world images demonstrate the efficacy of this approach.

Detection of microcalcifications in digital mammograms using wavelets

This paper presents an approach for detecting microcalcifications in digital mammograms employing wavelet-based subband image decomposition. The microcalcifications appear in small clusters of few pixels with relatively high intensity compared with their neighboring pixels. These image features can be preserved by a detection system that employs a suitable image transform which can localize the signal characteristics in the original and the transform domain. Given that the microcalcifications correspond to high-frequency components of the image spectrum, detection of microcalcifications is achieved by decomposing the mammograms into different frequency subbands, suppressing the low-frequency subband, and, finally, reconstructing the mammogram from the subbands containing only high frequencies. Preliminary experiments indicate that further studies are needed to investigate the potential of wavelet-based subband image decomposition as a tool for detecting microcalcifications in digital mammograms.

Region adaptive subband image coding

We present a region adaptive subband image coding scheme using the statistical properties of image subbands for various subband decompositions. Motivated by analytical results obtained when the input signal to the subband decomposition is a unit step function, we analyze the energy packing properties toward the lower frequency subbands, edges, and the dependency of energy distribution on the orientation of the edges, in subband decomposed images. Based on these investigations and ideal analysis/synthesis filtering done in the frequency domain, the region adaptive subband image coding scheme extracts suitably shaped regions in each subband and then uses adaptive entropy-constrained quantizers for different regions under the assumption of a generalized Gaussian distribution for the image subbands. We also address the problem of determining an optimal subband decomposition among all possible decompositions. Experimental results show that visual degradations in the reconstructed image are negligible at a bit rate of 1.0 b/pel and reasonable quality images are obtainable at rates as low as 0.25 b/pel.

On the influence of the phase of conjugate quadrature filters in subband image coding

The influence of the phase of conjugate quadrature filters (CQFs) on the performances of a subband coding scheme is analyzed. When the filter length is short, the phase characteristic has virtually no influence on the peak signal-to-noise ratio (PSNR)/bit rate results and on the performance of postprocessing algorithms such as edge detection.

Separability-based multiscale basis selection and feature extraction for signal and image classification

Algorithms for multiscale basis selection and feature extraction for pattern classification problems are presented. The basis selection algorithm is based on class separability measures rather than energy or entropy. At each level the "accumulated" tree-structured class separabilities obtained from the tree which includes a parent node and the one which includes its children are compared. The decomposition of the node (or subband) is performed (creating the children), if it provides larger combined separability. The suggested feature extraction algorithm focuses on dimensionality reduction of a multiscale feature space subject to maximum preservation of information useful for classification. At each level of decomposition, an optimal linear transform that preserves class separabilities and results in a reduced dimensional feature space is obtained. Classification and feature extraction is then performed at each scale and resulting "soft decisions" obtained for each area are integrated across scales. The suggested algorithms have been tested for classification and segmentation of one-dimensional (1-D) radar signals and two-dimensional (2-D) texture and document images. The same idea can be used for other tree structured local basis, e.g., local trigonometric basis functions, and even for nonorthogonal, redundant and composite basis dictionaries.

Image compression based on fuzzy algorithms for learning vector quantization and wavelet image decomposition

This work evaluates the performance of an image compression system based on wavelet-based subband decomposition and vector quantization. The images are decomposed using wavelet filters into a set of subbands with different resolutions corresponding to different frequency bands. The resulting subbands are vector quantized using the Linde-Buzo-Gray (LBG) algorithm and various fuzzy algorithms for learning vector quantization (FALVQ). These algorithms perform vector quantization by updating all prototypes of a competitive neural network through an unsupervised learning process. The quality of the multiresolution codebooks designed by these algorithms is measured on the reconstructed images belonging to the training set used for multiresolution codebook design and the reconstructed images from a testing set.

Image coding using robust quantization for noisy digital transmission

A robust quantizer is developed for encoding memoryless sources and transmission over the binary symmetric channel (BSC). The system combines channel optimized scalar quantization (COSQ) with all-pass filtering, the latter performed using a binary phase-scrambling/descrambling method. Applied to a broad class of sources, the robust quantizer achieves the same performance as the Gaussian COSQ for the memoryless Gaussian source. This quantizer is used in image coding for transmission over a BSC. The peak signal-to-noise ratio (PSNR) performance degrades gracefully as the channel bit error rate increases.

Visibility of wavelet quantization noise

The discrete wavelet transform (DWT) decomposes an image into bands that vary in spatial frequency and orientation. It is widely used for image compression. Measures of the visibility of DWT quantization errors are required to achieve optimal compression. Uniform quantization of a single band of coefficients results in an artifact that we call DWT uniform quantization noise; it is the sum of a lattice of random amplitude basis functions of the corresponding DWT synthesis filter. We measured visual detection thresholds for samples of DWT uniform quantization noise in Y, Cb, and Cr color channels. The spatial frequency of a wavelet is r 2-lambda, where r is display visual resolution in pixels/degree, and lambda is the wavelet level. Thresholds increase rapidly with wavelet spatial frequency. Thresholds also increase from Y to Cr to Cb, and with orientation from lowpass to horizontal/vertical to diagonal. We construct a mathematical model for DWT noise detection thresholds that is a function of level, orientation, and display visual resolution. This allows calculation of a "perceptually lossless" quantization matrix for which all errors are in theory below the visual threshold. The model may also be used as the basis for adaptive quantization schemes.

A segmentation-based lossless image coding method for high-resolution medical image compression

Lossless compression techniques are essential in archival and communication of medical images. In this paper, a new segmentation-based lossless image coding (SLIC) method is proposed, which is based on a simple but efficient region growing procedure. The embedded region growing procedure produces an adaptive scanning pattern for the image with the help of a very-few-bits-needed discontinuity index map. Along with this scanning pattern, an error image data part with a very small dynamic range is generated. Both the error image data and the discontinuity index map data parts are then encoded by the Joint Bi-level Image experts Group (JBIG) method. The SLIC method resulted in, on the average, lossless compression to about 1.6 h/pixel from 8 b, and to about 2.9 h/pixel from 10 b with a database of ten high-resolution digitized chest and breast images. In comparison with direct coding by JBIG, Joint Photographic Experts Group (JPEG), hierarchical interpolation (HINT), and two-dimensional Burg Prediction plus Huffman error coding methods, the SLIC method performed better by 4% to 28% on the database used.

Comparison of different methods of classification in subband coding of images

This paper investigates various classification techniques, applied to subband coding of images, as a way of exploiting the nonstationary nature of image subbands. The advantages of subband classification are characterized in a rate-distortion framework in terms of "classification gain" and overall "subband classification gain." Two algorithms, maximum classification gain and equal mean-normalized standard deviation classification, which allow unequal number of blocks in each class, are presented. The dependence between the classification maps from different subbands is exploited either directly while encoding the classification maps or indirectly by constraining the classification maps. The trade-off between the classification gain and the amount of side information is explored. Coding results for a subband image coder based on classification are presented. The simulation results demonstrate the value of classification in subband coding.

Subband-coded image reconstruction for lossy packet networks

Transmission of digital subband-coded images over lossy packet networks presents a reconstruction problem at the decoder. This paper presents two techniques for reconstruction of lost subband coefficients, one for low-frequency coefficients and one for high-frequency coefficients. The low-frequency reconstruction algorithm is based on inherent properties of the hierarchical subband decomposition. To maintain smoothness and exploit the high intraband correlation, a cubic interpolative surface is fit to known coefficients to interpolate lost coefficients. Accurate edge placement, crucial for visual quality, is achieved by adapting the interpolation grid in both the horizontal and vertical directions as determined by the edges present. An edge model is used to characterize the adaptation, and a quantitative analysis of this model demonstrates that edges can be identified by simply examining the high-frequency bands, without requiring any additional processing of the low-frequency band. High-frequency reconstruction is performed using linear interpolation, which provides good visual performance as well as maintains properties required for edge placement in the low-frequency reconstruction algorithm. The complete algorithm performs well on loss of single coefficients, vectors, and small blocks, and is therefore applicable to a variety of source coding techniques.

Space-frequency quantization for wavelet image coding

A new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with tree-structured quantization (related to spatial structures) has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical representation. This paper addresses the problem of how spatial quantization modes and standard scalar quantization can be applied in a jointly optimal fashion in an image coder. We consider zerotree quantization (zeroing out tree-structured sets of wavelet coefficients) and the simplest form of scalar quantization (a single common uniform scalar quantizer applied to all nonzeroed coefficients), and we formalize the problem of optimizing their joint application. We develop an image coding algorithm for solving the resulting optimization problem. Despite the basic form of the two quantizers considered, the resulting algorithm demonstrates coding performance that is competitive, often outperforming the very best coding algorithms in the literature.

Adaptive motion-compensated wavelet filtering for image sequence coding

This paper deals with new advances made in the field of discrete spatio-temporal filters applied to digital image sequences. Within time-varying images, the temporal correlation of the information is folded within the spatio-temporal domain by motions originating from both camera and object displacements. The spatio-temporal video information can be therefore reformulated in terms of motion trajectories and intensity variations along these trajectories. To yield that signal description, the spatio-temporal scenes will be segmented according to motion. Motion-compensated temporal filters have been used as convolutional filters applied along the assumed motion trajectories. Spectral interpretations show the efficiency of motion-compensated filtering for video signals. As a matter of fact, the whole signal analysis performed in this paper also includes a spatial filtering to achieve a complete spatio-temporal (2-D+T) decomposition. Motion-compensated filtering leads to multiresolution applications. It leads to optimum and adaptive signal-to-noise decomposition procedures based on the temporal correlative content. Such properties allow enhancing tasks like temporal interpolation, image sequence smoothing, and restoration. Simulation results are presented in this paper to illustrate the field of image sequence coding.

Digital color imaging

This paper surveys current technology and research in the area of digital color imaging. In order to establish the background and lay down terminology, fundamental concepts of color perception and measurement are first presented using vector-space notation and terminology. Present-day color recording and reproduction systems are reviewed along with the common mathematical models used for representing these devices. Algorithms for processing color images for display and communication are surveyed, and a forecast of research trends is attempted. An extensive bibliography is provided.

Advances in automated 3-D image analyses of cell populations imaged by confocal microscopy

Automated three-dimensional (3-D) image analysis methods are presented for rapid and effective analysis of populations of fluorescently labeled cells or nuclei in thick tissue sections that have been imaged three dimensionally using a confocal microscope. The methods presented here greatly improve upon our earlier work (Roysam et al.:J Microsc 173: 115-126, 1994). The principal advances reported are: algorithms for efficient data pre-processing and adaptive segmentation, effective handling of image anisotrophy, and fast 3-D morphological algorithms for separating overlapping or connected clusters utilizing image gradient information whenever available. A particular feature of this method is its ability to separate densely packed and connected clusters of cell nuclei. Some of the challenges overcome in this work include the efficient and effective handling of imaging noise, anisotrophy, and large variations in image parameters such as intensity, object size, and shape. The method is able to handle significant inter-cell, intra-cell, inter-image, and intra-image variations. Studies indicate that this method is rapid, robust, and adaptable. Examples were presented to illustrate the applicability of this approach to analyzing images of nuclei from densely packed regions in thick sections of rat liver, and brain that were labeled with a fluorescent Schiff reagent.

An entropy-coded lattice vector quantizer for transform and subband image coding

A lattice-based vector quantizer (VQ) and noiseless code are proposed for transform and subband image coding. The quantization is simple to implement, and no vector codebooks need to be stored. The noiseless code enumerates lattice codevectors based on their (weighted) l(1) norm. A software implementation is able to handle lattice codebooks of size 2(256). The image coding performance is shown to be comparable or superior to the best encoding methods reported in the literature.

Combining the discrete wavelet transform and mixed-domain filtering

A novel filtering method is proposed that combines the discrete orthogonal wavelet transform (DWT) with the mixed-domain (mixed-D) filtering method. The method uses the DWT to pre- and postprocess those dimensions of the signal that are transformed to the discrete-frequency domain by mixed-D filtering. Using the DWT in this manner provides a controlled mechanism to partition the spectrum of the input signal into subband signals, which then may be selectively filtered during the linear difference equation (LDE) step of the mixed-D algorithm. It is shown that, when the DWT is computed using filters with ideal high- and lowpass frequency responses, the LDE filters used in the mixed-D filtering stage are unchanged by the introduction of the DWT (although the frequency tuple associated with each LDE filter is altered). This indicates that the mixed-D filtering scheme can be easily used in subband coding systems. Results are given for the filtering of a three-dimensional (3-D) linear trajectory signal, representing a common application in video processing.

An image multiresolution representation for lossless and lossy compression

We propose a new image multiresolution transform that is suited for both lossless (reversible) and lossy compression. The new transformation is similar to the subband decomposition, but can be computed with only integer addition and bit-shift operations. During its calculation, the number of bits required to represent the transformed image is kept small through careful scaling and truncations. Numerical results show that the entropy obtained with the new transform is smaller than that obtained with predictive coding of similar complexity. In addition, we propose entropy-coding methods that exploit the multiresolution structure, and can efficiently compress the transformed image for progressive transmission (up to exact recovery). The lossless compression ratios are among the best in the literature, and simultaneously the rate versus distortion performance is comparable to those of the most efficient lossy compression methods.

A successive approximation vector quantizer for wavelet transform image coding

A coding method for wavelet coefficients of images using vector quantization, called successive approximation vector quantization (SA-W-VQ) is proposed. In this method, each vector is coded by a series of vectors of decreasing magnitudes until a certain distortion level is reached. The successive approximation using vectors is analyzed, and conditions for convergence are derived. It is shown that lattice codebooks are an efficient tool for meeting these conditions without the need for very large codebooks. Regular lattices offer the extra advantage of fast encoding algorithms. In SA-W-VQ, distortion equalization of the wavelet coefficients can be achieved together with high compression ratio and precise bit-rate control. The performance of SA-W-VQ for still image coding is compared against some of the most successful image coding systems reported in the literature. The comparison shows that SA-W-VQ performs remarkably well at several bit rates and in various test images.

Finite-state vector quantization by exploiting interband and intraband correlations for subband image coding

Subband coding (SBC) with vector quantization (VQ) has been shown to be an effective method for coding images at low bit rates. We split the image spectrum into seven nonuniform subbands. Threshold vector quantization (TVQ) and finite state vector quantization (FSVQ) methods are employed in coding the subband images by exploiting interband and intraband correlations. Our new SBC-FSVQ schemes have the advantages of the subband-VQ scheme while reducing the bit rate and improving the image quality. Experimental results are given and comparisons are made using our new scheme and some other coding techniques. In the experiments, it is found that SBC-FSVQ schemes achieve the best peak signal-to-noise ratio (PSNR) performance when compared to other methods at the same bit rate.

Multiplierless PR quadrature mirror filters for subband image coding

This correspondence deals with suboptimal multiplierless perfect reconstruction quadrature mirror filter (PR-QMF) solutions. It is shown that multiplierless PR-QMFs perform comparable to or better than the known filter banks and discrete-cosine-transform-based (DCT-based) image coding techniques objectively and subjectively. They are very efficient to implement on very large scale integrated (VLSI) systems. These PR-QMFs might find uses in real-time image and video coding and other applications.

Hierarchical partition priority wavelet image compression

Image compression methods for progressive transmission using optimal hierarchical decomposition, partition priority coding (PPC), and multiple distribution entropy coding (MDEC) are presented. In the proposed coder, a hierarchical subband/wavelet decomposition transforms the original image. The analysis filter banks are selected to maximize the reproduction fidelity in each stage of progressive image transmission. An efficient triple-state differential pulse code modulation (DPCM) method is applied to the smoothed subband coefficients, and the corresponding prediction error is Lloyd-Max quantized. Such a quantizer is also designed to fit the characteristics of the detail transform coefficients in each subband, which are then coded using novel hierarchical PPC (HPPC) and predictive HPPC (PHPPC) algorithms. More specifically, given a suitable partitioning of their absolute range, the quantized detail coefficients are ordered based on both their decomposition level and partition and then are coded along with the corresponding address map. Space filling scanning further reduces the coding cost by providing a highly spatially correlated address map of the coefficients in each PPC partition. Finally, adaptive MDEC is applied to both the DPCM and HPPC/PHPPC outputs by considering a division of the source (quantized coefficients) into multiple subsources and adaptive arithmetic coding based on their corresponding histograms. Experimental results demonstrate the great performance of the proposed compression methods.

A jointly optimized subband coder

The mainstream approach to subband coding has been to partition the input signal into subband signals and to code those signals separately with optimal or near-optimal quantizers and entropy coders. A more effective approach, however, is one where the subband coders are optimized jointly so that the average distortion introduced by the subband quantizers is minimized subject to a constraint on the output rate of the subband encoder. A subband coder with jointly optimized multistage residual quantizers and entropy coders is introduced and applied to image coding. The high performance of the coder is attributed to its ability to exploit statistical dependencies within and across the subbands. The efficiency of the multistage residual quantization structure and the effectiveness of the statistical modeling algorithm result in an attractive balance among the reproduction quality, rate, and complexity.