APPLICATION OF ITERATIVE ALGORITHMS TO ADAPTIVE PREDICTIVE CODING

Abstract

Application of various iterative algorithms to adaptive predictive coding (APC) of image data is described. The variable steepsize steepest descent (VSSD) algorithm, obtained by coupling the adaptive predictor to the adaptive quantizer (Mark, 1976), represents the best candidate in terms of system performance and system complexity. The Kalman algorithm exhibits fast convergence and good distortion measure, but is too complex for implementation. For grey level image coding, an adaptive Laplacian quantizer in conjunction with adaptive predictive coding exhibits superior performance to an adaptive Gaussian quantizer. APC coding of image data offers at least a 7dB improvement in SNR over optimum PCM at any quantization level.     

一种新的JPEG图像无参考客观质量评价方法

Parsval’s原理指出,图像压缩前、后像素值的均方误差值等同与图像压缩前、后DCT系数的均方误差值,根据这一思想设计了JPEG图像无参考客观质量评价算法。假设图像的DCT系数是Laplacian分布,首先根据JPEG图像的DCT系数估计出图像压缩前的DCT系数分布参数,并由此估算出图像压缩前、后DCT系数的均方误差值。实验结果表明,该方法所用指标能准确地描述JPEG图像的质量且与空间域均方误差指标相符。     

An efficient iterative algorithm for designing an asymptotically optimal modified unrestricted uniform polar quantization of bivariate Gaussian random variables

In this paper, a more efficient and a more accurate algorithm is developed for designing asymptotically optimal unrestricted uniform polar quantization (UUPQ) of bivariate Gaussian random variables compared to the existing algorithms on this subject. The proposed algorithm is an iterative one defining the analytical model of asymptotically optimal UUPQ in only a few iterations. The UUPQ model is also improved via optimization of the last magnitude reconstruction level so that the mean squared error (MSE) is minimal. Moreover, for the straightforward performance assessment of our analytical UUPQ model an asymptotic formula for signal to quantization noise ratio (SQNR) is derived, which is reasonably accurate for any rate (R) greater than or equal to 2.5 bits/sample. It is demonstrated empirically that our asymptotically optimal UUPQ model outperforms the previous UUPQ models in terms of SQNR. Eventually, the transition from the analytical to the practically designed UUPQ model, as an important aspect in quantizer design, is considered in the paper and, as a result, a novel method to achieve this is provided. The proposed method is applicable to the practical design of any unrestricted polar quantization.     

Image retrieval using color histograms generated by Gauss mixture vector quantization

Image retrieval based on color histograms requires quantization of a color space. Uniform scalar quantization of each color channel is a popular method for the reduction of histogram dimensionality. With this method, however, no spatial information among pixels is considered in constructing the histograms. Vector quantization (VQ) provides a simple and effective means for exploiting spatial information by clustering groups of pixels. We propose the use of Gauss mixture vector quantization (GMVQ) as a quantization method for color histogram generation. GMVQ is known to be robust for quantizer mismatch, which motivates its use in making color histograms for both the query image and the images in the database. Results show that the histograms made by GMVQ with a penalized log-likelihood (LL) distortion yield better retrieval performance for color images than the conventional methods of uniform quantization and VQ with squared error distortion.     

Optimal entropy-constrained non-uniform scalar quantizer design for low bit-rate pixel domain DVC

In this paper, an optimal entropy-constrained non-uniform scalar quantizer is proposed for the pixel domain DVC. The uniform quantizer is efficient for the hybrid video coding since the residual signals conforming to a single-variance Laplacian distribution. However, the uniform quantizer is not optimal for pixel domain distributed video coding (DVC). This is because the uniform quantizer is not adaptive to the joint distribution of the source and the SI, especially for low level quantization. The signal distribution of pixel domain DVC conforms to the mixture model with multi-variance. The optimal non-uniform quantizer is designed according to the joint distribution, the error between the source and the SI can be decreased. As a result, the bit rate can be saved and the video quality won’t sacrifice too much. Accordingly, a better R-D trade-off can be achieved. First, the quantization level is fixed and the optimal RD trade-off is achieved by using a Lagrangian function J(Q). The rate and distortion components is designed based on P(Y|Q). The conditional probability density function of SI Y depend on quantization partitions Q, P(Y|Q), is approximated by a Guassian mixture model at encocder. Since the SI can not be accessed at encoder, an estimation of P(Y|Q) based on the distribution of the source is proposed. Next, J(Q) is optimized by an iterative Lloyd-Max algorithm with a novel quantization partition updating algorithm. To guarantee the convergence of J(Q), the monotonicity of the interval in which the endpoints of the quantizer lie must be satisfied. Then, a quantizer partition updating algorithm which considers the extreme points of the histogram of the source is proposed. Consequently, the entropy-constrained optimal non-uniform quantization partitions are derived and a better RD trade-off is achieved by applying them. Experiment results show that the proposed scheme can improve the performance by 0.5 dB averagely compared to the uniform scalar quantization.     

A supervised learning neural network coprocessor for soft-decisionmaximum-likelihood decoding

A supervised learning neural network (SLNN) coprocessor which enhances the performance of a digital soft-decision Viterbi decoder used for forward error correction in a digital communication channel with either fading plus additive white Gaussian noise (AWGN) or pure AWGN has been investigated and designed. The SLNN is designed to cooperate with a phase shift keying (PSK) demodulator, an automatic gain control (AGC) circuit, and a 3-bit quantizer which is an analog to digital convertor. It is trained to learn the best uniform quantization step-size Delta (BEST) as a function of the mean and the standard deviation of various sets of Gaussian distributed random variables. The channel cutoff rate (R(0)) of the channel is employed to determine the best quantization threshold step-size (Delta(BEST)) that results in the minimization of the Viterbi decoder output bit error rate (BER). For a digital communication system with a SLNN coprocessor, consistent and substantial BER performance improvements are observed. The performance improvement ranges from a minimum of 9% to a maximum of 25% for a pure AWGN channel and from a minimum of 25% to a maximum of 70% for a fading channel. This neural network coprocessor approach can be generalized and applied to any digital signal processing system to decrease the performance losses associated with quantization and/or signal instability.     

压缩视频感知中量化器的研究与设计

压缩视频感知（Compressed Video Sensing,CVS）是一种利用压缩感知（Compressed Sensing,CS）以及分布式视频编码（DVC）的视频压缩方法,故又被称为分布式视频压缩感知。在CVS中,每帧图像经过块划分、压缩采样后对数据进行DPCM,最后使用均匀或者非均匀量化进行量化。目前,CVS量化器的设计大多是在采样数据或残差数据服从高斯分布的前提下设计的,通过Kolmogorov-Smirnov检验进一步分析压缩采样后的数据,利用劳埃德最佳量化器准则训练量化码书,设计出一种简单、高效的量化器。经实验,设计的量化器相比于传统的量化方法在BD-Rate上减少了约14.2%,在BDPSNR上提升了约0.11?dB,提高了CVS的压缩效率和重建质量。     

结合Gamma修正的色彩量化新算法

色彩量化的最终目的是使得视觉效果上的最化图像与原图像的差别（即失真）最小，量化的应用又对算法效率提出很高的要求，文中提出一种结合Gamma修正的量化算法，速度明显快于中位切分等以往算法，并且量化图像的质量近似于，甚至部分视觉效果优于这些算法，该算法是一种切实有效的图像量化方法，它在计算复杂度和量人结果的精确度上进行了折衷。     

Combining image compression and classification using vectorquantization

We describe a method of combining classification and compression into a single vector quantizer by incorporating a Bayes risk term into the distortion measure used in the quantizer design algorithm. Once trained, the quantizer can operate to minimize the Bayes risk weighted distortion measure if there is a model providing the required posterior probabilities, or it can operate in a suboptimal fashion by minimizing the squared error only. Comparisons are made with other vector quantizer based classifiers, including the independent design of quantization and minimum Bayes risk classification and Kohonen's LVQ. A variety of examples demonstrate that the proposed method can provide classification ability close to or superior to learning VQ while simultaneously providing superior compression performance     

随机性参数分布式量化估计及其最优比特分配

本文研究总比特率给定下随机向量参数分布式量化估计及其最优比特分配问题.与现有文献大都假定每个传感器的量化比特率给定而不是最优分配下研究随机性参数的分布式量化估计问题不同的是,本文将综合考虑最优量化器、最优估计器算法以及给定总比特率下的最优比特分配问题.针对向量状态标量观测模型,首先借助现有文献给出基于量化观测的最优估计器及其误差协方差阵形式表达,其次得到各传感器的渐近最优量化器实际为著名的Lloyd-max量化器,且各传感器的渐近最优量化级数与信噪比成正比,同时引入一种次优的求解非负整数比特率的方法.考虑到当传感器数目比较大时,初始的最优估计器算法运算量很大,设计了一种渐近等价的迭代量化估计器算法,其计算负担大大减轻,且对于存在延迟或丢包的网络环境亦适用,增强了算法的鲁棒性.仿真结果表明,本文提出的最优比特分配方案估计性能明显优于一般的均匀比特分配方案.     

An adaptive approach for the reduction of quantization errors†

This paper presents an adaptive quantization scheme for the reduction of the percentage error in the output of the quantizer. The improvement in the system performance is illustrated by simulating a uniform step and an adaptive quantizer on a digital computer and comparing their outputs. A significant improvement in the output is achieved by using the suggested scheme.     

Geometric piecewise uniform lattice vector quantization of the memoryless Gaussian source

The aim of this paper is to find a quantization technique that has low implementation complexity and asymptotic performance arbitrarily close to the optimum. More specifically, it is of interest to develop a new vector quantizer design procedure for a memoryless Gaussian source that yields vector quantizers with excellent performance and the structure required for fast quantization. To achieve this, we combined a fast lattice-encoding algorithm with a geometric approach to generate a model of a geometric piecewise-uniform lattice vector quantizer. Expressions for granular distortion and the optimal number of outputs points in each region were derived. Both exact and approximative asymptotic analyses were carried out. During this process, the constant probability density function of the input signal vector was kept inside the whole region. The analysis demonstrated the existence of piecewise-constant approximations to the input-vector probability density function, which is optimal for the proposed geometric piecewise-uniform vector quantizer. The considered quantization technique is near optimal for a memoryless Gaussian source. In other words, this paper proposes a method for a near-optimum, low-complex vector quantizer design based on probability density function discretization. The presented methodology gives a signal-to-quantization noise ratio that in some cases differs from the optimum by 0.1 dB or less. Improvements of the considered model in performance and complexity over some of the existing techniques are also demonstrated.     

A High-Rate Optimal Transform Coder With Gaussian Mixture Companders

This paper examines the problem of designing fixed-rate transform coders for sources whose distributions are unknown and presumably non-Gaussian, under input-weighted squared error distortion measures. As a component of this system, a flexible scalar compander based on Gaussian mixtures is proposed. The high-rate analysis of transform coders is reviewed, and extended to the case of input-weighted squared error. An algorithm is developed to set the parameters of the system using a data-driven technique that automatically balances the source statistics, distortion measure, and structure of the transform coder to minimize the high-rate distortion. The implementation of Gaussian mixture companders is explored, resulting in a flexible, low-complexity scalar quantizer. Additionally, modifications to the system for operation at moderate rates, using unstructured scalar quantizers, are presented. The operation of the system for the problem of wideband speech line spectral frequencies (LSF) quantization with log spectral distortion is illustrated, and shown to provide good performance with very low complexity     

随机性标量参数分布式量化的最优比特分配

本文研究了在总比特率设定的情况下,改良并给出表现更优的量化器,以及如何实现基于网络的随机标量参数分布式量化估计,重点讨论传感器比特数最优分配.与常规给定各传感器的量化比特率不同的是,本文将结合估计器算法使用和不同量化器的构建,来研究固定总比特率下的分配.文中的观测模型噪声服从高斯分布,并且以此模型为对象通过均匀量化探讨基于一般类型与线性估计器的最理想比特分配方式.前者均方误差上限与后者对应下限在高精度处理方案下结果几乎相同,都表现出网络中观测噪声误差反比于量化级数这一特性.此外还借用交替序列比特分配算法以确保求解出的数值解恒非负.最后从MATLAB仿真结果可以看到,本文给出的最优比特分配估计器较传统方案的表现更优.     

视频编码量化失真估值算法研究

针对量化失真估计算法存在的误差问题,对算法中的DCT系数分布模型进行了改进,提出了基于LAP分布模型的分段建模方法。将DCT系数的尾部数据进行分离,以主体数据的建模结果作为全体数据的分布模型。以均方误差作为量化失真的衡量准则,归纳并推到上述分布模型下的失真估计算法。采用限制量化步长的方法来评估失真估计算法的准确度。实验结果表明,采用LAP分布模型对DCT系数进行分段建模,不仅提高了模型的准确度,还简化了分布模型的复杂度;由此所产生的失真估计算法在复杂度和准确度方面具有很高的兼容性,与传统的LAP失真估计算法相比,准确度有所提高。     

基于均方误差的变形图像的质量评价

随着数字图像技术的发展图像质量评价已成为了一个重要的研究课题.作为图像质量的一部分,图像逼真度通常由均方误差来表示.均方误差作为既简单又古老的客观图像质量评价方法沿用至今,在图像质量评价中扮演着重要角色,但在实际应用过程中发现其存在一定的局限性.从对比度拉伸、亮度变化、加噪声、模糊、放缩、平移、旋转等经典图像变形的角度出发,实现了给定一个均方误差值和允许误差值,得到11种均方误差值近似相等的变形图像.经分析得出,同一均方误差下的不同变形图像给人的主观感受不同;图像经很小的几何修正后,对应的均方误差值可能很大;均方误差越大,图像失真越严重.并设计了一个120人的主观评价实验,验证了均方误差在基础变形图像上评价的局限性.     

基于多级SMVQ的图象编码算法

边缘匹配矢量量化器(SMVQ)是有限状态矢量量化器(FSVQ)的一个分支。该量化器适合于对图像块间相关性高的图像进行压缩编码,其优点是在比特率相近的情况下,编码质量高于传统的穷尽搜索矢量量化编码器,但其缺点是计算量大和比特率固定。本文提出了一种改进的边缘匹配矢量量化器。测试结果表明,该算法是变比特率编码算法,它比边缘匹配矢量量化器的比特率低,编码速度快,编码质量得到提高。     

JPEG压缩编码的扩充自适应量化器设计

在ＪＰＥＧ静止图象压缩的基础上，设计了一种扩充的自适应量化器，利用人眼的视觉特征，通过分析ＭＣＵ块的局部视觉活动性，以ＭＣＵ活动性涵数确定量化因子，并引入亮度掩盖算子调节量化参量，实验结果表明，本文所设计的自适应量化器能减少图象编码主观失真，改善了图象质量，获得更好的压缩效果。     

A sequential initialization technique for vector quantizer design

Vector quantization has been used in compressing both speech and image data. In theory, better performance can always be achieved by coding vectors instead of scalars. However, actual results depend upon the proper design of the quantizer. Vector quantizer design typically employs an algorithm such as the K-means algorithm or the Linde Buzo Gray algorithm in which the initialization affects the design cost (convergence rate) and the achievable performance (quantization error). After reviewing several current initialization techniques, a sequential initialization method called Error Function Initialization is presented. In this method, the seeds are chosen one at a time by attempting to maximize the step-wise reduction in the quantization error. Experimental results show that this technique yields faster convergence and smaller quantization errors. For real time applications, the technique could be used to design sub-optimal vector quantizers.     

State estimation for linear discrete-time systems using quantized measurements

In this paper, we consider the problem of state estimation for linear discrete-time dynamic systems using quantized measurements. This problem arises when state estimation needs to be done using information transmitted over a digital communication channel. We investigate how to design the quantizer and the estimator jointly. We consider the use of a logarithmic quantizer, which is motivated by the fact that the resulting quantization error acts as a multiplicative noise, an important feature in many applications. Both static and dynamic quantization schemes are studied. The results in the paper allow us to understand the tradeoff between performance degradation due to quantization and quantization density (in the infinite-level quantization case) or number of quantization levels (in the finite-level quantization case).