Showing papers by "William A. Pearlman published in 1995"

Data compression using set partitioning in hierarchical trees

Abstract: A data compression technique includes a subband decomposition of a source image followed by coding of the coefficients of the resultant subband decomposition for storage and/or transmission. During coding, three ordered lists are used comprising a list of significant pixels (LSP), a list of insignificant pixels (LIP) and a list of insignificant sets of pixels (LIS). The pixels in the LIP are tested, and those that are significant at a current quantization level are moved to the LSP. Similarly, sets are sequentially evaluated following the LIS order, and when a set is found to be significant it is removed from the LIS and partitioned into new subsets. The new subsets with more than one element are added back to the end of the LIS, while the single-coordinate sets are added to the end of the LIP or to the end of the LSP, depending whether they are insignificant or significant, respectively.

Variable-rate tree-structured vector quantizers

Abstract: In general, growth algorithms for optimal tree-structured vector quantizers do not exist. In this paper we show that if the source satisfies certain conditions; namely, that of diminishing marginal returns; optimal growth algorithms do exist. We present such an algorithm and compare its performance with that of other tree growth algorithms. Even for sources that do not meet the necessary conditions for the growth algorithm to be optimal, such as for speech with unknown statistics, it is seen by simulation that the algorithm outperforms other known growth algorithms, For sources that do not satisfy the required conditions, the algorithm presented here can also be used to grow the initial tree for the pruning process. The performance of such pruned trees is superior to that of trees pruned from full trees of the same rate. >

A clustering algorithm for entropy-constrained vector quantizer design with applications in coding image pyramids

Abstract: A clustering algorithm for the design of efficient vector quantizers to be followed by entropy coding is proposed. The algorithm, called entropy-constrained pairwise nearest neighbor (ECPNN), designs codebooks by merging the pair of Voronoi regions which gives the least increase in distortion for a given decrease in entropy. The algorithm can be used as an alternative to the entropy-constrained vector quantizer design (ECVQ) proposed by Chou, Lookabaugh, and Gray (1989). By a natural extension of the ECPNN algorithm the authors develop another algorithm that designs alphabet and entropy-constrained vector quantizers and call it alphabet- and entropy-constrained pairwise nearest neighbor (AECPNN) design. Through simulations on synthetic sources, it is shown that ECPNN and ECVQ have indistinguishable mean-square-error versus rate performance and that the ECPNN and AECPNN algorithms obtain as close performance by the same measure as the ECVQ and AECVQ (Rao and Pearlman, 1993) algorithms. The advantages over ECVQ are that the ECPNN approach enables much faster codebook design and uses smaller codebooks. A single pass through the ECPNN (or AECPNN) design algorithm, which progresses from larger to successively smaller rates, allows the storage of any desired number of intermediate codebooks. In the context of multirate subband (or transform) coders, this feature is especially desirable. The performance of coding image pyramids using ECPNN and AECPNN codebooks at rates from 1/3 to 1.0 bit/pixel is discussed. >

Orthogonalization of circular stationary vector sequences and its application to the Gabor decomposition

Abstract: Certain vector sequences in Hermitian or in Hilbert spaces, can be orthogonalized by a Fourier transform. In the finite-dimensional case, the discrete Fourier transform (DFT) accomplishes the orthogonalization. The property of a vector sequence which allows the orthogonalization of the sequence by the DFT, called circular stationarity (CS), is discussed in this paper. Applying the DFT to a given CS vector sequence results in an orthogonal vector sequence, which has the same span as the original one. In order to obtain coefficients of the decomposition of a vector upon a particular nonorthogonal CS vector sequence, the decomposition is first found upon the equivalent DFT-orthogonalized one and then the required coefficients are found through the DFT. It is shown that the sequence of discrete Gabor (1946) basis functions with periodic kernel and with a certain inner product on the space of N-periodic discrete functions, satisfies the CS condition. The theory of decomposition upon CS vector sequences is then applied to the Gabor basis functions to produce a fast algorithm for calculation of the Gabor coefficients. >

Information-theoretic performance of quadrature mirror filters

Abstract: Most existing quadrature mirror filters (QMFs) closely match the derived closed-form expression for an efficient class of QMFs. We use the closed-form expressions to derive the relationship between information-theoretic loss and the frequency selectivity of the QMF, by calculating first-order entropy as well as rate-distortion theoretic performance of a two band QMF system. We find that practical QMFs do not suffer a significant information-theoretic loss with first-order autoregressive Gaussian sources. With second-order autoregressive sources we find that practical QMFs suffer a notable information-theoretic loss when the bandwidth of the source is extremely narrow, but incur a small loss when the bandwidth is wider. We suggest that our results broadly apply to higher order autoregressive sources as well.

Improving the performance of optimal joint decoding

Abstract: The optimal joint decoder utilizing NLIVQ (nonlinear interpolative vector quantization) introduced by Gersho [1990] results in vector quantizers which have reduced encoding complexity at the expense of coding performance loss due to the inferiority of their space-filling property. We show a method of improving a high resolution NLIVQ codebook by partitioning its cells in such a way that the resulting lower resolution codebook consists of cells with better space-filling properties. The resolution reduction method is also extended to the case where the quantizer indices are entropy-constrained. From the simulations it is seen that the unconstrained and constrained entropy versions of the proposed vector quantizer have comparable performance to vector quantizers designed by LEG and ECVQ algorithms.

Image subband coding using an information-theoretic subband splitting criterion

Abstract: It has been proved recently that for Gaussian sources with memory an ideal subband split will produce a coding gain for scalar or vector quantization of the subbands. Following the methodology of the proofs, we outline a method for successively splitting the subbands of a source, one at a time to obtain the largest coding gain. The subband with the largest theoretical rate reduction (TRR) is determined and split at each step of the decomposition process. The TRR is the difference between the rate in optimal encoding of N-tuples from a Gaussian source (or subband) and the rate for the same encoding of its subband decomposition. The TRR is a monotone increasing function of a so-called spectral flatness ratio, which involves the products of the eigenvalues of the source (subband) and subband decomposition covariance matrices of order N. These eigenvalues are estimated by the variances of the Discrete Cosine Transform, which approximates those of the optimal Karhunen Loeve Transform. After the subband decomposition hierarchy or tree is determined through the criterion of maximal TRR, each subband is encoded with a variable rate entropy constrained vector quantizer. Optimal rate allocation to subbands is done with the BFOS algorithm which does not require any source modelling. We demonstrate the benefit of using the criterion by comparing coding results on a two-level low-pass pyramidal decomposition with coding results on a two-level decomposition obtained using the criterion. For 60 MCFD (Motion Compensated Frame Difference) frames of the Salesman sequence an average rate- distortion advantage of 0.73 dB and 0.02 bpp and for 30 FD (Frame Difference) frames of Caltrain image sequence an average rate-distortion advantage of 0.41 dB and 0.013 bpp are obtained with the optimal decomposition over low-pass pyramidal decomposition.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Adaptive joint rate allocation and quantization in subband signal coding

Abstract: We propose an elegant yet efficient adaptive subband coding scheme in which the rate allocation and structures of the quantizers are jointly optimized based on the time-varying rate-distortion characteristics of the input signals. By employing the tree-structured vector quantizers and the generalized BFOS pruning algorithm, the operations of the rate allocation and quantization are elegantly combined, whereby the adaptation is both convenient and optimal. The results on video coding have shown that the adaptive scheme can achieve substantial performance improvement over the non-adaptive scheme.