A practical suboptimal (variable source coding) algorithm for lossy data compression is presented. This scheme is based on approximate string matching, and it naturally extends the lossless Lempel-Ziv (1977) data compression scheme. Among others we consider the typical length of an approximately repeated pattern within the first n positions of a stationary mixing sequence where D percent of mismatches is allowed. We prove that there exists a constant r/sub 0/(D) such that the length of such an approximately repeated pattern converges in probability to 1/r/sub 0/(D) log n (pr.) but it almost surely oscillates between 1/r/sub -/spl infin//(D) log n and 2/r/sub 1/(D) log n, where r/sub -/spl infin//(D)>r/sub 0/(D)>r/sub 1/(D)/2 are some constants. These constants are natural generalizations of Renyi entropies to the lossy environment. More importantly, we show that the compression ratio of a lossy data compression scheme based on such an approximate pattern matching is asymptotically equal to r/sub 0/(D). We also establish the asymptotic behavior of the so-called approximate waiting time N/sub l/ which is defined as the time until a pattern of length C repeats approximately for the first time. We prove that log N/sub l//l/spl rarr/r/sub 0/(D) (pr.) as l/spl rarr//spl infin/. In general, r/sub 0/(D)>R(D) where R(D) is the rate distortion function. Thus for stationary mixing sequences we settle in the negative the problem investigated by Steinberg and Gutman by showing that a lossy extension of the Wyner-Ziv (1989) scheme cannot be optimal.

/pdf/a-suboptimal-lossy-data-compression-based-on-approximate-32hpmhusls.pdf

A suboptimal lossy data compression based on approximate pattern matching

In this paper, we survey some of the recent advances in lossless compression of continuous-tone images. The modeling paradigms underlying the state-of-the-art algorithms, and the principles guiding their design, are discussed in a unified manner. The algorithms are described and experimentally compared.

http://www.hpl.hp.com/techreports/2000/HPL-2000-163.pdf

Lossless compression of continuous-tone images

http://www02.smt.ufrj.br/~eduardo/papers/mmp_journal.pdf

Multidimensional signal compression using multiscale recurrent patterns

We propose a non-transform image compression scheme based on approximate 1D pattern matching, called pattern matching image compression (PMIC). The main idea behind it is a lossy extension of the Lempel-Ziv data compression scheme in which one searches for the longest prefix of an uncompressed image that approximately occurs in the already processed image. This main algorithm is enhanced with several new features such as searching for reverse approximate matching, recognizing sub-strings in images that are additively shifted versions of each other, introducing a variable and adaptive maximum distortion level D, and so forth. These enhancements are crucial to the overall quality of our scheme and their efficient implementation leads to algorithmic issues of interest in their own right. Both algorithmic and experimental results are presented. Our scheme turns out to be competitive with JPEG and wavelet compression for good quality graphical images. We also review related theoretical results.

/pdf/pattern-matching-image-compression-algorithmic-and-empirical-512rzo002h.pdf

Pattern matching image compression: algorithmic and empirical results

Lossless image compression has traditionally employed techniques quite separate from those used for text compression or lossy image compression; most standards employ modeling followed by coding (e.g., the JBIG standard, the IBM Q-coder, CCITT Group 4). Constantinescu and Storer [1994] presented a lossy image compression scheme that can be viewed as a generalization of lossless dynamic dictionary compression ("LZ2" type methods) to two dimensions with approximate matching; Constantinescu and Storer [1995] have experimented with this approach for lossless image compression with great success. Here we generalize "LZ1" type methods to lossless image compression. We examine complexity issues and 2D implementations.

Lossless image compression using generalized LZ1-type methods

Constantinescu and Storer presented a new single-pass adaptive vector quantization algorithm that learns a codebook of variable size and shape entries; they presented experiments on a set of test images showing that with no training or prior knowledge of the data, for a given fidelity, the compression achieved typically equals or exceeds that of the JPEG standard. This paper presents improvements in speed (by employing K-D trees), simplicity of codebook entries, and visual quality with no loss in either the amount of compression or the SNR as compared to the original full-search version. >

J.A. Storer

Papers

Improved techniques for single-pass adaptive vector quantization