Image coding by matching pursuit and perceptual pruning

The matching pursuit algorithm has been successfully applied in many areas such as data compression and pattern recognition. The performance of matching pursuit is closely related to the selection of the dictionary. In this paper, we propose an algorithm to estimate the optimal dictionary distribution ratio and discuss the decay of the norm of residual signal in matching pursuit when the coefficients are quantized by a uniform scalar quantizer. It is proposed that if the approximation error E and the dimension of the space N are given, the optimal size of the dictionary and the optimal quantizer step should be obtained by minimizing the number of bits required to store the matching pursuit representation of any signal in the space to satisfy the error bound.

Embedded quantization is a mechanism through which image coding systems provide quality progressivity. Although the most common embedded quantization approach is to use uniform scalar dead zone quantization (USDQ) together with bit plane coding (BPC), recent work suggested that similar coding performance as that achieved with USDQ+BPC can be obtained with a general embedded quantization (GEQ) scheme than performs fewer quantization stages. Unfortunately, practical approaches of GEQ can not be implemented in bit plane coding engines without substantially modifying their structure. This work overcomes this drawback introducing a 2-step scalar dead zone quantization (2SDQ) scheme compatible with bit plane image coding that provides the same advantages of practical GEQ approaches. Herein, 2SDQ is introduced in the framework of JPEG2000 to demonstrate its viability and efficiency.

We introduce an image coding algorithm in which perceptual pruning is used to select the most perceptually relevant image components. The algorithm uses a new maximum likelihood based image indistinguishability criterion that derives from a cortical snapshot, which is a model of the response of striate cortical simple cells to the image at a given point of fixation. The criterion must be satisfied at all points of fixation. We demonstrate that this method selects image components in a better way than matching pursuit and show image coding results of high subjective quality at low encoding rates.

∞A new wavelet-based L∞-constrained fixed and embedded coding technique is proposed. The embedded bit stream can be truncated for any desired distortion bound at a corresponding bit rate, so that the target upper bound on the elements of the reconstruction error signal is guaranteed. The original image can also be coded up to a fixed a priori user-defined distortion bound, ranging up to lossless coding. A lifting-based wavelet decorrelating transform is employed on the original image, and exact relations are established between spatial and wavelet domain distortions. The wavelet coefficients are quantized by symmetric uniform quantizers for fixed-distortion coding and by families of embedded uniform deadzone scalar quantizers for embedded coding. The quantized coefficients are finally losslessly encoded using a quadtree-based coding algorithm. Any floating-point lifting-based wavelet transform can be used, and a few of the popular wavelet transforms included in the JPEG2000 verification model are worked out as examples. We compare other L∞-constrained coding schemes and show that our proposed coder offers in addition a fully embedded L∞-oriented bit stream. We illustrate also that the proposed coder retains the same capabilities as the state-of-the-art embedded wavelet-based codecs, while providing superior compression results and embeddedness with respect to the L distortion measure.

Studies the asymptotic characteristics of uniform scalar quantizers that are optimal with respect to mean-squared error (MSE). When a symmetric source density with infinite support is sufficiently well behaved, the optimal step size /spl Delta//sub N/ for symmetric uniform scalar quantization decreases as 2/spl sigma/N/sup -1/V~/sup -1/(1/6N/sup 2/), where N is the number of quantization levels, /spl sigma//sup 2/ is the source variance and V~/sup -1/(/spl middot/) is the inverse of V~(y)=y/sup -1/ /spl int//sub y//sup /spl infin// P(/spl sigma//sup -1/X>x) dx. Equivalently, the optimal support length N/spl Delta//sub N/ increases as 2/spl sigma/V~/sup -1/(1/6N/sup 2/). Granular distortion is asymptotically well approximated by /spl Delta//sub N//sup 2//12, and the ratio of overload to granular distortion converges to a function of the limit /spl tau//spl equiv/lim/sub y/spl rarr//spl infin//y/sup -1/E[X|X>y], provided, as usually happens, that /spl tau/ exists. When it does, its value is related to the number of finite moments of the source density, an asymptotic formula for the overall distortion D/sub N/ is obtained, and /spl tau/=1 is both necessary and sufficient for the overall distortion to be asymptotically well approximated by /spl Delta//sub N//sup 2//12. Applying these results to the class of two-sided densities of the form b|x|/sup /spl beta//e(-/spl alpha/|x|/sup /spl alpha//), which includes Gaussian, Laplacian, Gamma, and generalized Gaussian, it is found that /spl tau/=1, that /spl Delta//sub N/ decreases as (ln N)/sup 1//spl alpha///N, that D/sub N/ is asymptotically well approximated by /spl Delta//sub N//sup 2//12 and decreases as (ln N)/sup 2//spl alpha///N/sup 2/, and that more accurate approximations to /spl Delta//sub N/ are possible. The results also apply to densities with one-sided infinite support, such as Rayleigh and Weibull, and to densities whose tails are asymptotically similar to those previously mentioned.

This paper reports improvements in compression of both inter- and intra-frame images by the matching pursuits (MP) algorithm. For both types of image, applying a 2D wavelet decomposition prior to MP coding is beneficial. The MP algorithm is then applied using various separable ID codebooks. MERGE coding with precision limited quantization (PLQ) is used to yield a highly embedded data stream. For inter-frames (residuals) a codebook of only 8 bases with compact footprint is found to give improved fidelity at lower complexity than previous MP methods. Great improvement is also achieved in MP coding of still images (intra-frames). Compared to JPEG 2000, lower distortion is achieved on the residual images tested, and also on intra-frames at low bit rates.

Matching pursuit is a powerful and flexible optimisation technique that has found applications in different areas, including image and video compression. This paper proposes an underlying probabilistic model for the entropy coding of the parameters generated by the matching pursuit algorithm in the context of image coding. It also distinguishes between orthogonal and fully-orthogonal matching pursuit, and provides a formulation for rate-distortion optimized matching pursuit.

In this paper, we provide operational rate-distortion results for memoryless generalized Gaussian sources. Close approximations of the entropy are provided for these sources, after a uniform scalar quantization at low/high resolution. Asymptotic expressions of the distortion for an arbitrary p-th order error measure are also given. The resulting approximations at low/high bitrate of the operational rate-distortion function are thus compared with the Shannon optimal bound showing the overall good performance of uniform quantization rules.

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.

The statistical properties of the error in uniform scalar quantization have been analyzed by a number of authors in the past, and is a well-understood topic today. The analysis has also been extended to the case of dithered quantizers, and the advantages and limitations of dithering have been studied and well documented in the literature. Lattice vector quantization is a natural extension into multiple dimensions of the uniform scalar quantization. Accordingly, there is a natural extension of the analysis of the quantization error. It is the purpose of this paper to present this extension and to elaborate on some of the new aspects that come with multiple dimensions. We show that, analogous to the one-dimensional case, the quantization error vector can be rendered independent of the input in subtractive vector-dithering. In this case, the total mean square error is a function of only the underlying lattice and there are lattices that minimize this error. We give a necessary condition on such lattices. In nonsubtractive vector dithering, we show how to render moments of the error vector independent of the input by using appropriate dither random vectors. These results can readily be applied for the case of wide sense stationary (WSS) vector random processes, by use of iid dither sequences. We consider the problem of pre- and post-filtering around a dithered lattice quantifier, and show how these filters should be designed in order to minimize the overall quantization error in the mean square sense. For the special case where the WSS vector process is obtained by blocking a WSS scalar process, the optimum prefilter matrix reduces to the blocked version of the well-known scalar half-whitening filter.

We present a lossless coding procedure based on a recently introduced decorrelating scheme, where both intra- and interchannel redundancies are removed by lossless prediction. The resulting signals are scalar entropy coded. We show that for continuous-amplitude Gaussian sources discretized with uniform scalar quantizers, no suboptimality occurs in the proposed lossless coding scheme by using scalar instead of vector entropy coders, except from a term caused by the lossless constraint, which vanishes in the limit of small distortions. This lossless constraint is described in terms of excess bit rate. The proposed coder may be used either as a compressor, or as a scalable lossless coder. In this case, a multistage version of the lossless coder based on ADPCM-like lossless prediction loops allows one to transmit the data by means of substreams, which represent different resolution levels. We show that this multiresolution approach is slightly suboptimal in comparison with a single global compression because of the noise feedback created in the ADPCM-like loops, but not of the space filling loss of the scalar quantizers. We propose a strategy to fix the stepsizes of these quantizers so that the delivered rates approach some predetermined target rates.

We propose a scheme for rate-constrained distributed nonparametric regression using a wireless sensor network. The scheme is universal across a wide range of sensor noise models, including unbounded and nonadditive noise; it has low complexity, requiring simple operations such as uniform scalar quantization with dither and message passing between neighboring nodes in the network, and attains minimax optimality for regression functions in common smoothness classes. We present theoretical results on the tradeoff between the compression rate, communication complexity of encoding, and the MSE and demonstrate empirical performance of the scheme using simulations.

In this paper a detail analysis of speech coding algorithm based on forward adaptive technique is carried out. We consider an algorithm that works on frame-by-frame basis, where a frame consists of a certain number of speech samples. Buffering frame-by-frame an estimation of the gain defined as squared root of the frame variance is enabled. The information about the gain (side information) and the code book of a nonadaptive quantizer, which is designed for the unit variance case of the input signal, are further used when designing an adaptive quantizer. In such a way better quantizer adaptation to the varying input statistics is provided. Observe that the goal of this paper is to investigate the preference that for the wide range of variance change could be achieved when implementing in the forward adaptive speech coding algorithm, the recently developed effective method for the Lloyd-Max's algorithm initialization, which provides optimal Lloyd-Max's quantizer performances for the unit variance case of the input signal. We destine to consider the speech coding algorithm based on forward adaptive technique since the backward adaptation provides SQNR (signal to quantization noise ratio) within 1 dB of the forward adaptation. We provide theoretical and experimental results (performances of our algorithm) which are compared with the optimal results. Additionally, we discuss the performances of speech coding schemes designed according to G. 711 standard and we point out the benefits that can be achieved by using our algorithm. Finally, in order to find better solution for implementation of the proposed algorithm in practice we consider the performances of our algorithm when log-uniform as well as uniform scalar quantizer are used for gain quantizing.

This paper studies the asymptotic characteristics of optimal fixed-rate uniform scalar quantizers for source densities with infinite support. Asymptotic formulas for the optimal step size and the resulting minimum mean-squared error are given. It is found that the asymptotic significance of overload distortion is directly related to the limit of y/sup -1/E[X|X>y] as y tends to infinity.

This paper deals with the problem of image retrieval when the database is presented in a compressed form, by using typically the JPEG2000 encoding scheme based on wavelet transform followed by an uniform scalar quantization. The state-of-the-art method aims at applying a preprocessing step before the feature extraction to reduce the difference in the compression qualities between the images. Our contribution consists in extracting robust features directly from the quantized coefficients. More precisely, assuming that the unquantized coefficients within a subband have a Laplacian distribution, we propose to estimate the distribution parameter from the quantized coefficients. Then, the estimated parameters of the whole subbands are used to build a salient feature for the indexing process. Experimental results show that the proposed retrieval approach significantly improves the state-of-the-art one.