Constrained-storage quantization of multiple vector sources bycodebook sharing

A codebook sharing technique, called constrained storage vector quantization (CSVQ), is introduced. This technique offers a convenient and optimal way of trading off performance against storage. The technique can be used in conjunction with tree-structured vector quantization (VQ) and other structured VQ techniques that alleviate the search complexity obstacle. The effectiveness of CSVQ is illustrated for coding transform coefficients of audio signals with multistage VQ     

Constrained-storage vector quantization with a universal codebook

Many image compression techniques require the quantization of multiple vector sources with significantly different distributions. With vector quantization (VQ), these sources are optimally quantized using separate codebooks, which may collectively require an enormous memory space. Since storage is limited in most applications, a convenient way to gracefully trade between performance and storage is needed. Earlier work addressed this problem by clustering the multiple sources into a small number of source groups, where each group shares a codebook. We propose a new solution based on a size-limited universal codebook that can be viewed as the union of overlapping source codebooks. This framework allows each source codebook to consist of any desired subset of the universal code vectors and provides greater design flexibility which improves the storage-constrained performance. A key feature of this approach is that no two sources need be encoded at the same rate. An additional advantage of the proposed method is its close relation to universal, adaptive, finite-state and classified quantization. Necessary conditions for optimality of the universal codebook and the extracted source codebooks are derived. An iterative design algorithm is introduced to obtain a solution satisfying these conditions. Possible applications of the proposed technique are enumerated, and its effectiveness is illustrated for coding of images using finite-state vector quantization, multistage vector quantization, and tree-structured vector quantization.     

A differential index assignment scheme for tree-structured vectorquantization

A differential index (DI) assignment scheme is proposed for the image encoding system in which a variable-length tree-structured vector quantizer (VLTSVQ) is adopted. Each source vector is quantized into a terminal node of VLTSVQ and each terminal node is represented as a unique binary vector. The proposed index assignment scheme utilizes the correlation between interblocks of the image to increase the compression ratio with the image quality maintained. Simulation results show that the proposed scheme achieves a much higher compression ratio than the conventional one does and that the amount of the bit rate reduction of the proposed scheme becomes large as the correlation of the image becomes large. The proposed encoding scheme can be effectively used to encode MR images whose pixel values are, in general, highly correlated with those of the neighbor pixels.     

Trellis-based scalar vector quantization of sources with memory

The trellis-based scalar-vector quantizer (TB-SVQ) can achieve the rate-distortion performance bound for memoryless sources. This paper extends the scope of this quantizer to coding of sources with memory. First considered is a simple extension, called the predictive TB-SVQ, which applies a closed-loop predictive coding operation in each survivor path of the Viterbi codebook search algorithm. Although the predictive TB-SVQ outperforms all other known structured fixed-rate vector quantizers, due to practical reasons, it may not approach the rate-distortion limit. A new quantization scheme motivated by the precoding idea of Laroia et al. (1993), called the precoded TB-SVQ, is also considered; the granular gain is realized by the underlying trellis code while the combination of the precoder and the SVQ structure provides the boundary gain. This new quantization scheme is asymptotically optimal and can, in principle, approach the rate-distortion bound for Markov sources     

Adaptive entropy-coded pruned tree-structured predictive vectorquantization of images

Simpler versions of a previously introduced adaptive entropy-coded predictive vector quantization (PVQ) scheme where the embedded entropy constrained vector quantizer (ECVQ) is replaced by a pruned tree-structured VQ (PTSVQ) are described. The resulting encoding scheme is shown to result in drastically reduced complexity at only a small cost in performance. Coding results for selected real-world images are given     

Reduced storage VQ via secondary quantization

This paper introduces methods for reducing the table storage required for encoding and decoding with unstructured vector quantization (UVQ) or tree-structured vector quantization (TSVQ). Specifically, a low-storage secondary quantizer is used to compress the code vectors (and test vectors) of the primary quantizer. The relative advantages of uniform and nonuniform secondary quantization are investigated. A Linde-Buzo-Gray (LBG) like algorithm that optimizes the primary UVQ codebook for a given secondary codebook and another that jointly optimizes both primary and secondary codebooks are presented. In comparison to conventional methods, it is found that significant storage reduction is possible (typically a factor of two to three) with little loss of signal-to-noise ratio (SNR). Moreover, when reducing dimension is considered as another method of reducing storage, it is found that the best strategy is a combination of both. The method of secondary quantization is also applied to TSVQ to reduce the table storage required for both encoding and decoding. It is shown that by exploiting the correlation among the test vectors in the tree, both encoder and decoder storage can be significantly reduced with little loss of SNR, by a factor of about four (or two) relative to the conventional method of storing test vectors (or test hyperplanes)     

Alphabet-constrained vector quantization

Alphabet-constrained rate-distortion theory is extended to coding of sources with memory. Two different cases are considered: when only the size of the codebook is constrained and when the codevector values are also held fixed. For both cases, nth-order constrained-alphabet rate-distortion functions are defined and a convergent algorithm for their evaluation is presented. Specific simulations using AR(1) sources show that performance near the rate-distortion bound is possible using a reproduction alphabet consisting of a small number of codevectors. It is also shown that the additional constraint of holding the codevector values fixed does not degrade performance of the coder in relation to the size-only constrained case. This observation motivates the development of a fixed-codebook vector quantizer, called the alphabet- and entropy-constrained vector quantizer, the performance of which is comparable to the entropy-constrained vector quantizer. A number of examples using an AR(1) and a speech source are presented to corroborate the theory     

Optimal pruning with applications to tree-structured source codingand modeling

An algorithm introduced by L. Breiman et al. (1984) in the context of classification and regression trees is reinterpreted and extended to cover a variety of applications in source coding and modeling in which trees are involved. These include variable-rate and minimum-entropy tree-structured vector quantization, minimum expected cost decision trees, variable-order Markov modeling, optimum bit allocation, and computer graphics and image processing using quadtrees. A concentration on the first of these and a detailed analysis of variable-rate tree-structured vector quantization are provided. It is found that variable-rate tree-structured vector quantization outperforms not only the fixed-rate variety but also full-search vector quantization. The successive approximation character of variable-rate tree-structured vector quantization permits it to degrade gracefully if the rate is reduced at the encoder. This has applications to the problem of buffer overflow     

Use of nonlinear principal component analysis and vectorquantization for image coding

The nonlinear principal component analysis (NLPCA) method is combined with vector quantization for the coding of images. The NLPCA is realized using the backpropagation neural network (NN), while vector quantization is performed using the learning vector quantizer (LVQ) NN. The effects of quantization in the quality of the reconstructed images are then compensated by using a novel codebook vector optimization procedure.     

Sample-adaptive product quantization: asymptotic analysis andexamples

Vector quantization (VQ) is an efficient data compression technique for low bit rate applications. However the major disadvantage of VQ is that its encoding complexity increases dramatically with bit rate and vector dimension. Even though one can use a modified VQ, such as the tree-structured VQ, to reduce the encoding complexity, it is practically infeasible to implement such a VQ at a high bit rate or for large vector dimensions because of the huge memory requirement for its codebook and for the very large training sequence requirement. To overcome this difficulty, a structurally constrained VQ called the sample-adaptive product quantizer (SAPQ) has recently been proposed. We extensively study the SAPQ that is based on scalar quantizers in order to exploit the simplicity of scalar quantization. Through an asymptotic distortion result, we discuss the achievable performance and the relationship between distortion and encoding complexity. We illustrate that even when SAPQ is based on scalar quantizers, it can provide VQ-level performance. We also provide numerical results that show a 2-3 dB improvement over the Lloyd-Max (1982, 1960) quantizers for data rates above 4 b/point     

Unified variable-length transform coding and image-adaptive vectorquantization

The authors introduce an image coding method which unifies two image coding techniques: variable-length transform coding (VLTC) and image-adaptive vector quantization (IAVQ). In both VLTC and IAVQ, the image is first decomposed into a set of blocks. VLTC encodes each block in the transform domain very efficiently: however, it ignores the interblock correlation completely. IAVQ addresses the interblock correlation by using a codebook generated from a subset of the blocks to vector-quantize all blocks. Although the resulting codebook represents the input image better than a universal codebook generated from a large number of training images, it has to be transmitted separately as an overhead, therefore degrading the coding performance at high bit rates     

Fast sequential implementation of “neural-gas” networkfor vector quantization

Although the “neural-gas” network proposed by Martinetz et al. in 1993 has been proven for its optimality in vector quantizer design and has been demonstrated to have good performance in time-series prediction, its high computational complexity (NlogN) makes it a slow sequential algorithm. We suggest two ideas to speedup its sequential realization: (1) using a truncated exponential function as its neighborhood function and (2) applying a new extension of the partial distance elimination method (PDE). This fast realization is compared with the original version of the neural-gas network for codebook design in image vector quantization. The comparison indicates that a speedup of five times is possible, while the quality of the resulting codebook is almost the same as that of the straightforward realization     

Pruned tree-structured vector quantisation with dead zones

The authors present pruned tree-structured vector quantisation with dead zones (PTSVQWDZ) which is suitable for transforming image or speech coding. PTSVQWDZ considerably improves the rate-distortion performance with a significantly reduced codebook storage when compared with the conventional PTSVQ     

Interpolative vector quantization of color images

Interpolative vector quantization has been devised to alleviate the visible block structure of coded images plus the sensitive codebook problems produced by a simple vector quantizer. In addition, the problem of selecting color components for color picture vector quantization is discussed. Computer simulations demonstrate the success of this coding technique for color image compression at approximately 0.3 b/pel. Some background information on vector quantization is provided     

A structured fixed-rate vector quantizer derived from avariable-length scalar quantizer. I. Memoryless sources

A low-complexity, fixed-rate structured vector quantizer for memoryless sources is described. This quantizer is referred to as the scalar-vector quantizer (SVQ), and the structure of its codebook is derived from a variable-length scalar quantizer. Design and implementation algorithms for this quantizer are developed and bounds on its performance are provided. Simulation results show that performance close to that of the optimal entropy-constrained scalar quantizer is possible with the fixed-rate quantizer. The SVQ is also robust against channel errors and outperforms both Lloyd-Max and entropy-constrained scalar quantizers for a wide range of channel error probabilities     

Variable rate vector quantization for medical image compression

Three techniques for variable-rate vector quantizer design are applied to medical images. The first two are extensions of an algorithm for optimal pruning in tree-structured classification and regression due to Breiman et al. The code design algorithms find subtrees of a given tree-structured vector quantizer (TSVQ), each one optimal in that it has the lowest average distortion of all subtrees of the TSVQ with the same or lesser average rate. Since the resulting subtrees have variable depth, natural variable-rate coders result. The third technique is a joint optimization of a vector quantizer and a noiseless variable-rate code. This technique is relatively complex but it has the potential to yield the highest performance of all three 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.     

一种针对ISF参数的量化算法

宽带语音编码中普遍使用导抗谱频率描述声道。利用转换分类差矢量分裂矢量量化方法对导抗谱频率进行量化,该方法基于转换分类矢量量化及差值分裂矢量量化。IsF矢量先按照给出的码书分类,然后每一类中的差矢量再进行分裂矢量量化。实验结果表明,该算法可在每帧编码比特数为37时达到透明量化要求,并且码书存储量明显少于StephenSo等人给出的转换分类分裂矢量量化方法。     

Three-dimensional subband coding of video

We describe and show the results of video coding based on a three-dimensional (3-D) spatio-temporal subband decomposition. The results include a 1-Mbps coder based on a new adaptive differential pulse code modulation scheme (ADPCM) and adaptive bit allocation. This rate is useful for video storage on CD-ROM. Coding results are also shown for a 384-kbps rate that are based on ADPCM for the lowest frequency band and a new form of vector quantization (geometric vector quantization (GVQ)) for the data in the higher frequency bands. GVQ takes advantage of the inherent structure and sparseness of the data in the higher bands. Results are also shown for a 128-kbps coder that is based on an unbalanced tree-structured vector quantizer (UTSVQ) for the lowest frequency band and GVQ for the higher frequency bands. The results are competitive with traditional video coding techniques and provide the motivation for investigating the 3-D subband framework for different coding schemes and various applications.     

Conditional entropy-constrained residual VQ with application toimage coding

This paper introduces an extension of entropy constrained residual vector quantization (VQ) where intervector dependencies are exploited. The method, which we call conditional entropy-constrained residual VQ, employs a high-order entropy conditioning strategy that captures local information in the neighboring vectors. When applied to coding images, the proposed method is shown to achieve better rate-distortion performance than that of entropy-constrained residual vector quantization with less computational complexity and lower memory requirements, moreover, it can be designed to support progressive transmission in a natural way. It is also shown to outperform some of the best predictive and finite-state VQ techniques reported in the literature. This is due partly to the joint optimization between the residual vector quantizer and a high order conditional entropy coder as well as the efficiency of the multistage residual VQ structure and the dynamic nature of the prediction.