Variable-length constrained-storage tree-structured vectorquantization

Constrained storage vector quantization, (CSVQ), introduced by Chan and Gersho (1990, 1991) allows for the stagewise design of balanced tree-structured residual vector quantization codebooks with low encoding and storage complexities. On the other hand, it has been established by Makhoul et al. (1985), Riskin et al. (1991), and by Mahesh et al. (see IEEE Trans. Inform. Theory, vol.41, p.917-30, 1995) that variable-length tree-structured vector quantizer (VLTSVQ) yields better coding performance than a balanced tree-structured vector quantizer and may even outperform a full-search vector quantizer due to the nonuniform distribution of rate among the subsets of its input space. The variable-length constrained storage tree-structured vector quantization (VLCS-TSVQ) algorithm presented in this paper utilizes the codebook sharing by multiple vector sources concept as in CSVQ to greedily grow an unbalanced tree structured residual vector quantizer with constrained storage. It is demonstrated by simulations on test sets from various synthetic one dimensional (1-D) sources and real-world images that the performance of VLCS-TSVQ, whose codebook storage complexity varies linearly with rate, can come very close to the performance of greedy growth VLTSVQ of Riskin et al. and Mahesh et al. The dramatically reduced size of the overall codebook allows the transmission of the code vector probabilities as side information for source adaptive entropy coding.     

Multiplication free vector quantization usingL1 distortion measure and its variants

The author considers vector quantization that uses the L (1) distortion measure for its implementation. A gradient-based approach for codebook design that does not require any multiplications or median computation is proposed. Convergence of this method is proved rigorously under very mild conditions. Simulation examples comparing the performance of this technique with the LBG algorithm show that the gradient-based method, in spite of its simplicity, produces codebooks with average distortions that are comparable to the LBG algorithm. The codebook design algorithm is then extended to a distortion measure that has piecewise-linear characteristics. Once again, by appropriate selection of the parameters of the distortion measure, the encoding as well as the codebook design can be implemented with zero multiplications. The author applies the techniques in predictive vector quantization of images and demonstrates the viability of multiplication-free predictive vector quantization of image data.     

Universal trellis coded quantization

A new form of trellis coded quantization based on uniform quantization thresholds and "on-the-fly" quantizer training is presented. The universal trellis coded quantization (UTCQ) technique requires neither stored codebooks nor a computationally intense codebook design algorithm. Its performance is comparable with that of fully optimized entropy-constrained trellis coded quantization (ECTCQ) for most encoding rates. The codebook and trellis geometry of UTCQ are symmetric with respect to the trellis superset. This allows sources with a symmetric probability density to be encoded with a single variable-rate code. Rate allocation and quantizer modeling procedures are given for UTCQ which allow access to continuous quantization rates. An image coding application based on adaptive wavelet coefficient subblock classification, arithmetic coding, and UTCQ is presented. The excellent performance of this coder demonstrates the efficacy of UTCQ. We also present a simple scheme to improve the perceptual performance of UTCQ for certain imagery at low bit rates. This scheme has the added advantage of being applied during image decoding, without the need to reencode the original image.     

Linearly constrained generalized Lloyd algorithm for reducedcodebook vector quantization

As linearly constrained vector quantization (LCVQ) is efficient for block-based compression of images that require low complexity decompression, it is a “de facto” standard for three-dimensional (3-D) graphics cards that use texture compression. Motivated by the lack of an efficient algorithm for designing LCVQ codebooks, the generalized Lloyd (1982) algorithm (GLA) for vector quantizer (VQ) codebook improvement and codebook design is extended to a new linearly constrained generalized Lloyd algorithm (LCGLA). This LCGLA improves VQ codebooks that are formed as linear combinations of a reduced set of base codewords. As such, it may find application wherever linearly constrained nearest neighbor (NN) techniques are used, that is, in a wide variety of signal compression and pattern recognition applications that require or assume distributions that are locally linearly constrained. In addition, several examples of linearly constrained codebooks that possess desirable properties such as good sphere packing, low-complexity implementation, fine resolution, and guaranteed convergence are presented. Fast NN search algorithms are discussed. A suggested initialization procedure halves iterations to convergence when, to reduce encoding complexity, the encoder considers the improvement of only a single codebook for each block. Experimental results for image compression show that LCGLA iterations significantly improve the PSNR of standard high-quality lossy 6:1 LCVQ compressed images     

Unitary space vector quantization codebook design for spatial correlated limited feedback MIMO system

In the transmitting, beamforming, and receiving combing （TBRC） MIMO system, a codebook based feedback strategy is usually used to provide the transmitter with the beamforming vector. The adopted codebook affects the system performance considerably. Therefore, the codebook design is a key technology in the TBRC MIMO system. In this article, the unitary space vector quantization （USVQ） codebook design criterion is proposed to design optimal codebooks for various spatial correlated MIMO channels. And the unitary space K-mean （USK） codebook generating algorithm is provided to generate the USVQ codebooks. Simulations show that the capacities of the feedback based TBRC systems using USVQ codebooks are very close to those of the ideal cases.     

Grassmannian beamforming for MIMO amplify-and-forward relaying

We consider the problem of beamforming codebook design for limited feedback half-duplex multiple-input multiple output (MIMO) amplify-and-forward (AF) relay system. In the first part of the paper, the direct link between the source and the destination is ignored. Assuming perfect channel state information (CSI), we show that the source and the relay should map their signals to the dominant right singular vectors of the source-relay and relay-destination channels. For the limited feedback scenario, we prove the appropriateness of Grassmannian codebooks as the source and relay beamforming codebooks based on the distributions of the optimal source and relay beamforming vectors. In the second part of the paper, the direct link is considered in the problem model. Assuming perfect CSI, we derive the optimization problem that identifies the optimal source beamforming vector and show that the solution to this problem is uniformly distributed on the unit sphere for independent and identically distributed (i.i.d) Rayleigh channels. For the limited feedback scenario, we justify the appropriateness of Grassmannian codebooks for quantizing the optimal source beamforming vector based on its distribution. Finally, a modified quantization scheme is presented, which introduces a negligible penalty in the system performance but significantly reduces the required number of feedback bits.     

Finite-state vector quantization for waveform coding

A finite-state vector quantizer is a finite-state machine used for data compression: Each successive source vector is encoded into a codeword using a minimum distortion rule, and into a code book, depending on the encoder state. The current state and the selected codeword then determine the next encoder state. A finite-state vector quantizer is capable of making better use of the memory in a source than is an ordinary memoryless vector quantizer of the same dimension or blocklength. Design techniques are introduced for finite-state vector quantizers that combine ad hoc algorithms with an algorithm for the design of memoryless vector quantizers. Finite-state vector quantizers are designed and simulated for Gauss-Markov sources and sampled speech data, and the resulting performance and storage requirements are compared with ordinary memoryless vector quantization.     

Next-state functions for finite-state vector quantization

The finite-state vector quantization scheme called dynamic finite-state vector quantization (DFSVQ) is investigated with regard to its subcodebook construction. In the DFSVQ, each input block is encoded by a small codebook called the subcodebook which is created from a much larger codebook called supercodebook. Each subcodebook is constructed by selecting, using a reordering procedure, a set of appropriate code-vectors from the supercodebook. The performance of the DFSVQ depends on this reordering procedure; therefore, several reordering procedures are introduced and their performance are evaluated. The reordering procedures investigated, are based on the conditional histogram of the code-vectors, index prediction, vector prediction, nearest neighbor design, and the frequency usage of the code-vectors. The performance of the reordering procedures are evaluated by comparing their hit ratios (the number of blocks encoded by the subcodebook) and their computational complexity. Experimental results are presented and it is found that the reordering procedure based on the vector prediction performs the best when compared with the other reordering procedures.     

Color quantization and processing by Fibonacci lattices

Color quantization is sampling of three-dimensional (3-D) color spaces (such as RGB or Lab) which results in a discrete subset of colors known as a color codebook or palette. It is extensively used for display, transfer, and storage of natural images in Internet-based applications, computer graphics, and animation. We propose a sampling scheme which provides a uniform quantization of the Lab space. The idea is based on several results from number theory and phyllotaxy. The sampling algorithm is very much systematic and allows easy design of universal (image-independent) color codebooks for a given set of parameters. The codebook structure allows fast quantization and ordered dither of color images. The display quality of images quantized by the proposed color codebooks is comparable with that of image-dependent quantizers. Most importantly, the quantized images are more amenable to the type of processing used for grayscale ones. Methods for processing grayscale images cannot be simply extended to color images because they rely on the fact that each gray-level is described by a single number and the fact that a relation of full order can be easily established on the set of those numbers. Color spaces (such as RGB or Lab) are, on the other hand, 3-D. The proposed color quantization, i.e., color space sampling and numbering of sampled points, makes methods for processing grayscale images extendible to color images. We illustrate possible processing of color images by first introducing the basic average and difference operations and then implementing edge detection and compression of color quantized images.     

Residual vector quantization using a multilayer competitive neuralnetwork

This paper presents a new technique for designing a jointly optimized residual vector quantizer (RVQ). In conventional stage-by-stage design procedure, each stage codebook is optimized for that particular stage distortion and does not consider the distortion from the subsequent stages. However, the overall performance can be improved if each stage codebook is optimized by minimizing the distortion from the subsequent stage quantizers as well as the distortion from the previous stage quantizers. This can only be achieved when stage codebooks are jointly designed for each other. In this paper, the proposed codebook design procedure is based on a multilayer competitive neural network where each layer of this network represents one stage of the RVQ. The weight connecting these layers form the corresponding stage codebooks of the RVQ. The joint design problem of the RVQ's codebooks (weights of the multilayer competitive neural network) is formulated as a nonlinearly constrained optimization task which is based on a Lagrangian error function. This Lagrangian error function includes all the constraints that are imposed by the joint optimization of the codebooks. The proposed procedure seeks a locally optimal solution by iteratively solving the equations for this Lagrangian error function. Simulation results show an improvement in the performance of an RVQ when designed using the proposed joint optimization technique as compared to the stage-by-stage design, where both generalized Lloyd algorithm (GLA) and the Kohonen learning algorithm (KLA) were used to design each stage codebook independently, as well as the conventional joint-optimization technique     

模糊强化学习型的图像矢量量化算法

本文给出了一种新的图像矢量量化码书的优化设计方法.传统矢量量化方法只考虑了码字与训练矢量之间的吸引影响,所以约束了最优解的寻解空间.本文提出了一种新的学习机理--模糊强化学习机制,该机制在传统的吸引因子基础上,引入新的排斥因子,极大地释放了吸引因子对最优解的寻解空间的约束.新的模糊强化学习机制没有采用引入随机扰动的方法来避免陷入局部最优码书,而是通过吸引因子和排斥因子的合力作用,较准确地确定了每个码字的最佳移动方向,从而使整体码书向全局最优解靠近.实验结果表明,基于模糊强化学习机制的矢量量化算法始终稳定地取得显著优于模糊K-means算法的性能,较好地解决了矢量量化中的码书设计容易陷入局部极小和初始码书影响优化结果的问题.     

Enhanced multistage vector quantization by joint codebook design

Multistage vector quantization (MSVQ) can achieve very low encoding and storage complexity in comparison to unstructured vector quantization. However, the conventional stage-by-stage design of the codebooks in MSVQ is suboptimal with respect to the overall performance measure. The authors introduce an algorithm for the joint design of the stage codebooks to optimize the overall performance. The performance improvement, although modest, is achieved with no effect on encoding or storage complexity and only a slight increase in design effort     

Block transform image coding by multistage vector quantization withoptimal bit allocation

A multistage vector quantization with optimal bit allocation (MVQ-OBA) in the transform domain is presented. A set of bit allocation planes is first obtained by slicing a (scalar) optimal bit allocation map where the number of bits assigned to each coefficient is proportional to the coefficient variance. The set of bit allocation planes determines the coefficients to be used and the codebook size at each stage. The vector dimensionalities are restricted to small values and relatively small codebooks are used, thus reducing both the overhead required for transmitting the codebooks and the complexity in codebook design. The computer simulation results demonstrate that MVQ-OBA is competitive with many other transform coding techniques including variable length transform coding. MVQ-OBA is well suited for progressive transmission     

Fast Image Coding Algorithm Using Indirect-Index Codebook Based on SMVQ

Side-match vector quantization (SMVQ) achieves better compression performance than vector quantization (VQ) in image coding due to its exploration of the dependence of adjacent pixels. However, SMVQ has the disadvantage of requiring excessive time during the process of coding. Therefore, this paper proposes a fast image coding algorithm using indirect-index codebook based on SMVQ (ⅡC-SMVQ) to reduce the coding time. Two codebooks, named indirect-index codebook (Ⅱ-codebook) and entire-state codebook (ES-codebook), are trained and utilized. The Ⅱ-codebook is trained by using the Linde-Buzo-Gray (LBG) algorithm from side-match information, while the ES-codebook is generated from the clustered residual blocks on the basis of the Ⅱ-codebook. According to the relationship between these two codebooks, the codeword in the Ⅱ-codebook can be regarded as an indicator to construct a fast search path, which guides in quickly determining the state codebook from the ES-codebook to encode the to-be-encoded block. The experimental results confirm that the coding time of the proposed scheme is shorter than that of the previous SMVQ.     

Partial distortion sensitive competitive learning algorithm foroptimal codebook design

An effective competitive learning algorithm based on the partial distortion theorem is proposed for optimal codebook design. Compared with some representative learning algorithms for codebook design, the proposed algorithm has consistently shown the best performance for designing codebooks of different sizes, especially large size codebooks     

Predictive residual vector quantization [image coding]

This paper presents a new vector quantization technique called predictive residual vector quantization (PRVQ). It combines the concepts of predictive vector quantization (PVQ) and residual vector quantization (RVQ) to implement a high performance VQ scheme with low search complexity. The proposed PRVQ consists of a vector predictor, designed by a multilayer perceptron, and an RVQ that is designed by a multilayer competitive neural network. A major task in our proposed PRVQ design is the joint optimization of the vector predictor and the RVQ codebooks. In order to achieve this, a new design based on the neural network learning algorithm is introduced. This technique is basically a nonlinear constrained optimization where each constituent component of the PRVQ scheme is optimized by minimizing an appropriate stage error function with a constraint on the overall error. This technique makes use of a Lagrangian formulation and iteratively solves a Lagrangian error function to obtain a locally optimal solution. This approach is then compared to a jointly designed and a closed-loop design approach. In the jointly designed approach, the predictor and quantizers are jointly optimized by minimizing only the overall error. In the closed-loop design, however, a predictor is first implemented; then the stage quantizers are optimized for this predictor in a stage-by-stage fashion. Simulation results show that the proposed PRVQ scheme outperforms the equivalent RVQ (operating at the same bit rate) and the unconstrained VQ by 2 and 1.7 dB, respectively. Furthermore, the proposed PRVQ outperforms the PVQ in the rate-distortion sense with significantly lower codebook search complexity.     

近似最近邻搜索中投影增强型残差量化方法

为了降低图像特征向量量化的近似表示和高维向量带来的码书训练时间开销，提出了一种投影增强型残差量化方法。在前期的增强型残差量化工作基础上，将主成分分析与增强型残差量化相结合，使得码书训练和特征量化均在低维向量空间进行以提高效率；在低维向量空间上训练码书过程中，提出了联合优化方法，同时考虑投影和量化产生的总体误差，提升码书精度；针对该量化方法，设计了一种特征向量之间的近似欧氏距离快速计算方法用于近似最近邻完全检索。结果表明，相比增强型残差量化，在相同检索精度前提条件下，投影增强型残差量化的只需花费近1/3的训练时间；相比其它同类方法，所提出方法在码书训练时间效率、检索速度和精度上均具有更优的综合性能。该研究为主成分分析同其它量化模型的有效结合提供了参考。     

Design, performance, and complexity analysis of residualtrellis-coded vector quantizers

Multistage trellis-coded vector quantization (MS-TCVQ) is developed as a constrained trellis source-coding technique. The performance of the two-stage TCVQ is studied for Gaussian sources. Issues of stage-by-stage design, output alphabet selection, and complexity are addressed with emphasis on selecting and partitioning the stage codebooks. For a given rate, MS-TCVQ achieves low encoding and storage complexity compared to TCVQ, and comparisons with same-dimensional multistage vector quantization indicate a 0.5-3-dB improvement in signal-to-quantization-noise ratio     

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

This paper 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 (1980) 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.