A vector quantizer with minimum visible distortion

A method for designing codebooks for vector quantization (VQ) based on minimum error visibility in a reconstructed picture is described. The method uses objective measurements to define visibility for the picture being coded. The proposed VQ is switched type, i.e., the codebook is divided into subcodebooks, each of which is related to a given subrange of error visibility. Codebook optimization is carried out on the basis of a particular definition of visible distortion of the reconstructed image. Subjective judgment of the test results, carried out at 0.5 b/pel bit rate, indicates that the proposed VQ enables low-distortion images to be reconstructed even when subcodebooks with a small number of codewords are used, thus reducing the codebook search time to about 10% of that required by a fixed VQ (both inside and outside the training set)     

二维网格编码矢量量化及其在静止图像量化中的应用

该文提出了在二维码书空间中，在矢量量化（VQ）的基础上，应用网格编码量化（TCQ）的思想来实现量化的新方法－－二维网格编码矢量量化（2D－TCVQ）。该方法首先把小码书扩展成大的虚码书，然后用网格编码矢量量化（TCVQ）的方法在扩大的二维码书空间中用维物比算法来寻找最佳量化路径。码书扩大造成第一子集最小失真减小从提高了量化性能。由于二维TCVQ采用的码书尺寸较小，因而可以应用到低存贮、低功耗的编解码环境。仿真结果表明，同一码书尺寸下，二维TCVQ比TCVQ好0．5dB左右。同时，该方法具有计算量适中，解码简单以及对误差扩散不敏感的优点。     

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     

基于仿射变换的改进型矢量量化编码

本文提出了基于仿射变换的改进型矢量量化编码算法，并给出了两种不同的实用结构，与传统矢量量化算法相比，该方法在不需要重新训练新码本及不增加码本存储空间的情况下，降低了编码误差，使得重建图像的ＰＳＮＲ显著增加，图像的主观质量也得到很大的改善。     

Pseudo-Gray coding

A pseudo-Gray code is an assignment of n-bit binary indexes to 2" points in a Euclidean space so that the Hamming distance between two points corresponds closely to the Euclidean distance. Pseudo-Gray coding provides a redundancy-free error protection scheme for vector quantization (VQ) of analog signals when the binary indexes are used as channel symbols on a discrete memoryless channel and the points are signal codevectors. Binary indexes are assigned to codevectors in a way that reduces the average quantization distortion introduced in the reproduced source vectors when a transmitted index is corrupted by channel noise. A globally optimal solution to this problem is generally intractable due to an inherently large computational complexity. A locally optimal solution, the binary switching algorithm, is introduced, based on the objective of minimizing a useful upper bound on the average system distortion. The algorithm yields a significant reduction in average distortion, and converges in reasonable running times. The sue of pseudo-Gray coding is motivated by the increasing need for low-bit-rate VQ-based encoding systems that operate on noisy channels, such as in mobile radio speech communications     

A complexity reduction technique for image vector quantization

A technique for reducing the complexity of spatial-domain image vector quantization (VQ) is proposed. The conventional spatial domain distortion measure is replaced by a transform domain subspace distortion measure. Due to the energy compaction properties of image transforms, the dimensionality of the subspace distortion measure can be reduced drastically without significantly affecting the performance of the new quantizer. A modified LBG algorithm incorporating the new distortion measure is proposed. Unlike conventional transform domain VQ, the codevector dimension is not reduced and a better image quality is guaranteed. The performance and design considerations of a real-time image encoder using the techniques are investigated. Compared with spatial domain a speed up in both codebook design time and search time is obtained for mean residual VQ, and the size of fast RAM is reduced by a factor of four. Degradation of image quality is less than 0.4 dB in PSNR.     

A robust joint source channel coding scheme for image transmission over the ionospheric channel

In this paper, we propose a joint source channel coding (JSCC) scheme to the transmission of fixed images for wireless communication applications. The ionospheric channel which presents some characteristics identical to those found on mobile radio channels, like fading, multipath and Doppler effect is our test channel. As this method based on a wavelet transform, a self-organising map (SOM) vector quantization (VQ) optimally mapped on a QAM digital modulation and an unequal error protection (UEP) strategy, this method is particularly well adapted to low bit-rate applications. The compression process consists in applying a SOM VQ on the discrete wavelet transform coefficients and computing several codebooks depending on the sub-images preserved. An UEP is achieved with a correcting code applied on the most significant data. The JSCC consists of an optimal mapping of the VQ codebook vectors on a high spectral efficiency digital modulation. This feature allows preserving the topological organization of the codebook along the transmission chain while keeping a reduced complexity system. This method applied on grey level images can be used for colour images as well. Several tests of transmission for different images have shown the robustness of this method even for high bit error rate (BER>10⁻²). In order to qualify the quality of the image after transmission, we use a PSNR% (peak signal-to-noise ratio) parameter which is the value of the difference of the PSNR after compression at the transmitter and after reception at the receiver. This parameter clearly shows that 95% of the PSNR is preserved when the BER is less than 10⁻².     

Optimization of requantization codebook for vector quantization.

Requantization is a key technology for reducing the bit rate of a previously compressed data. When recompression ratio is high, the requantizer may cause unacceptable quality degradation. To improve the quality of the requantized image, an optimization scheme for the requantization codebook has been proposed. The proposed scheme constructs an optimal requantization codebook in an iterative manner for a given original quantization codebook of transmitter. The construction of codebook is iteratively repeated until they reach a local optimum solution. Our approach can be applied not only to the scalar quantization, but to any method which employs vector quantization-based system. Simulation results show that the optimized system based on the proposed algorithm outperforms the conventional system which is made without consideration of requantization. The proposed algorithm enables a reliable image communication over heterogeneous networks.     

A fractal vector quantizer for image coding

We investigate the relation between VQ (vector quantization) and fractal image coding techniques, and propose a novel algorithm for still image coding, based on fractal vector quantization (FVQ). In FVQ, the source image is approximated coarsely by fixed basis blocks, and the codebook is self-trained from the coarsely approximated image, rather than from an outside training set or the source image itself. Therefore, FVQ is capable of eliminating the redundancy in the codebook without any side information, in addition to exploiting the self-similarity in real images effectively. The computer simulation results demonstrate that the proposed algorithm provides better peak signal-to-noise ratio (PSNR) performance than most other fractal-based coders.     

Adjacent Channel Interference Cancellation Using Orthogonal Precoding for Fractional Sampling OFDM Receiver

To achieve diversity with a single antenna, fractional sampling has been proposed. The imaging component of a desired signal must be transmitted by increasing the baseband filter bandwidth. This paper proposes and evaluates a system in which the imaging component is transmitted on the adjacent channel to the desired signal. The adjacent channel interference is cancelled by the precoding generated based on the basis of the channel state information of all the terminals. In this paper, the performance with perfect feedback and limited feedback is evaluated. Numerical results obtained through computer simulation show that the proposed scheme with a 6 bit random codebook for QPSK modulation improves the performance compared with that with the conventional scheme in the low $E_b/N_0$ region.     

A VLSI architecture for real-time image coding using a vectorquantization based algorithm

Digital image coding using vector quantization (VQ) based techniques provides low-bit rates and high quality coded images, at the expense of intensive computational demands. The computational requirement due to the encoding search process, had hindered application of VQ to real-time high-quality coding of color TV images. Reduction of the encoding search complexity through partitioning of a large codebook into the on-chip memories of a concurrent VLSI chip set is proposed. A real-time vector quantizer architecture for encoding color images is developed. The architecture maps the mean/quantized residual vector quantizer (MQRVQ) (an extension of mean/residual VQ) onto a VLSI/LSI chip set. The MQRVQ contributes to the feasibility of the VLSI architecture through the use of a simple multiplication free distortion measure and reduction of the required memory per code vector. Running at a clock rate of 25 MHz the proposed hardware implementation of this architecture is capable of real-time processing of 480×768 pixels per frame with a refreshing rate of 30 frames/s. The result is a real-time high-quality composite color image coder operating at a fixed rate of 1.12 b per pixel     

基于自组织特征映射的图像矢量量化研究

本文从自组织特征映射（ＳＯＦＭ）的基本思想出发，通过研究Ｋｏｈｏｎｅｎ网的输出节点在一维、二维和八维空间中不同排列方式，得到了相应的矢量量化（ＶＱ）码书设计算法。研究表明ＳＯＦＭ具有许多优点：可以设计出具有规则结构的码书，相邻码矢量具有较强的相关性；网络输出节点的不同排列方式对矢量量化器性能有较大影响，通过选择合适的排列方式，设计出的矢量量化器具有良好的抗信道误码能力。实验表明基于ＳＯＦＭ算法的矢     

一种低反馈开销多用户MIMO-OFDM系统功率最小化方案

该文利用凸规划理论中的库恩-塔克条件,为基于TCM编码的多用户MIMO-OFDM系统中实时业务资源优化问题提出了一种低反馈开销的功率最小化方案。该方案首先设计速率、功率和等效信道量化门限的码本,然后根据当前的信道状态信息分配子载波并对等效信道增益量化,最后基站给用户广播资源分配结果。仿真结果表明:相比其它方案,该文提出的方案有效降低系统能耗并且具有反馈开销低的特点。     

Quantization Methods for Equal Gain Transmission With Finite Rate Feedback

We consider the design and analysis of quantizers for equal gain transmission (EGT) systems with finite rate feedback-based communication in flat-fading multiple input single output (MISO) systems. EGT is a beamforming technique that maximizes the MISO channel capacity when there is an equal power-per-antenna constraint at the transmitter, and requires the feedback of t-1 phase angles, when there are t antennas at the transmitter. In this paper, we contrast two popular approaches for quantizing the phase angles: vector quantization (VQ) and scalar quantization (SQ). On the VQ side, using the capacity loss with respect to EGT with perfect channel information at transmitter as performance metric, we develop a criterion for designing the beamforming codebook for quantized EGT (Q-EGT). We also propose an iterative algorithm based on the well-known generalized Lloyd algorithm, for computing the beamforming vector codebook. On the analytical side, we study the performance of Q-EGT and derive closed-form expressions for the performance in terms of capacity loss and outage probability in the case of i.i.d. Rayleigh flat-fading channels. On the SQ side, assuming uniform scalar quantization and i.i.d. Rayleigh flat-fading channels, we derive the high-resolution performance of quantized EGT and contrast the performance with that of VQ. We find that although both VQ and SQ achieve the same rate of convergence (to the capacity with perfect feedback) as the number of feedback bits B increases, there exists a fixed gap between the two     

Sequential scalar quantization of vectors: an analysis

Proposes an efficient vector quantization (VQ) technique called sequential scalar quantization (SSQ). The scalar components of the vector are individually quantized in a sequence, with the quantization of each component utilizing conditional information from the quantization of previous components. Unlike conventional independent scalar quantization (ISQ), SSQ has the ability to exploit intercomponent correlation. At the same time, since quantization is performed on scalar rather than vector variables, SSQ offers a significant computational advantage over conventional VQ techniques and is easily amenable to a hardware implementation. In order to analyze the performance of SSQ, the authors appeal to asymptotic quantization theory, where the codebook size is assumed to be large. Closed-form expressions are derived for the quantizer mean squared error (MSE). These expressions are used to compare the asymptotic performance of SSQ with other VQ techniques. The authors also demonstrate the use of asymptotic theory in designing SSQ for a practical application (color image quantization), where the codebook size is typically small. Theoretical and experimental results show that SSQ far outperforms ISQ with respect to MSE while offering a considerable reduction in computation over conventional VQ at the expense of a moderate increase in MSE.     

Fast planar-oriented ripple search algorithm for hyperspace VQ codebook.

This paper presents a fast codebook search method for improving the quantization complexity of full-search vector quantization (VQ). The proposed method is built on the planar Voronoi diagram to label a ripple search domain. Then, the appropriate codeword can easily be found just by searching the local region instead of global exploration. In order to take a step further and obtain the close result full-search VQ would, we equip the proposed method with a duplication mechanism that helps to bring down the possible quantizing distortion to its lowest level. According to the experimental results, the proposed method is indeed capable of providing better outcome at a faster quantization speed than the existing partial-search methods. Moreover, the proposed method only requires a little extra storage for duplication.     

Fine-coarse vector quantization

A fast method for searching an unstructured vector quantization (VQ) codebook is introduced and analyzed. The method, fine-coarse vector quantization (FCVQ), operates in two stages: a `fine' structured VQ followed by a table lookup `coarse' unstructured VQ. Its rate, distortion, arithmetic complexity, and storage are investigated using analytical and experimental means. Optimality condition and an optimizing algorithm are presented. The results of experiments with both uniform scalar quantization and tree-structured VQ (TSVQ) as the first stage are reported. Comparisons are made with other fast approaches to vector quantization, especially TSVQ. It is found that when rate, distortion, arithmetic complexity, and storage are all taken into account, FCVQ outperforms TSVQ in a number of cases. In comparison to full search quantization, FCVQ has much lower arithmetic complexity, at the expense of a slight increase in distortion and a substantial increase in storage. The increase in mean-squared error (over full search) decays as a negative power of the available storage     

Dynamic finite-state vector quantization of digital images

A vector quantization (VQ) scheme with finite memory called dynamic finite-state vector quantization (DFSVQ) is presented. The encoder consists of a large codebook, so called super-codebook, where for each input vector a fixed number of its codevectors are chosen to generate a much smaller codebook (sub-codebook). This sub-codebook represents the best matching codevectors that could be found in the super-codebook for encoding the current input vector. The choice for the codevectors in the sub-codebook is based on the information obtained from the previously encoded blocks where directional conditional block probability (histogram) matrices are used in the selection of the codevectors. The index of the best matching codevector in the sub-codebook is transmitted to the receiver. An adaptive DFSVQ scheme is also proposed in which, when encoding an input vector, first the sub-codebook is searched for a matching codevector to satisfy a pre-specified waveform distortion. If such a codevector is not found in tile current sub-codebook then the whole super-codebook is checked for a better match. If a better match is found then a signaling flag along with the corresponding index of the codevector is transmitted to the receiver. Both the DFSVQ encoder and its adaptive version are implemented. Experimental results for several monochrome images with a super-codebook size of 256 or 512 and different sub-codebook sizes are presented     

应用神经网络的图像分类矢量量化编码

矢量量化作为一种有效的图像数据压缩技术，越来越受到人们的重视。设计矢量量化器的经典算法ＬＢＧ算法，由于运算复杂，从而限制了矢量量化的实用性。本文讨论了应用神经网络实现的基于边缘特征分类的矢量量化技术。它是根据人的视觉系统对图象的边缘的敏感性，应用模式识别技术，在对图像编码前，以边缘为特征对图像内容分类，然后再对每类进行矢量量化。除特征提取是采用离散余弦变换外，图像的分类和矢量量化都是由神经网络完成     

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