Information rates of autoregressive processes

The rate distortion functionR(D)is calculated for two time-discrete autoregressive sources--the time-discrete Gaussian autoregressive source with a mean-square-error fidelity criterion and the binary-symmetric first-order Markov source with an average probability-of-error per bit fidelity criterion. In both cases it is shown thatR(D)is bounded below by the rate distortion function of the independent-letter identically distributed sequence that generates the autoregressive source. This lower bound is shown to hold with equality for a nonzero region of small average distortion. The positive coding theorem is proved for the possibly nonstationary Gaussian autoregressive source with a constraint on the parameters. Finally, it is shown that the rate distortion function of any time-discrete autoregressive source with a difference distortion measure can be bounded below by the rate distortion function of the independent-letter identically distributed generating sequence with the same distortion measure.     

Perceptual quality metric for digital video coding

A new perceptually significant block-edge impairment metric as a quantitative distortion measure for blocking artifacts in digital video coding is presented. This distortion metric does not require the original image sequence as a comparative reference, and is found to be consistent with subjective evaluation.     

A metric for ARMA processes

Autoregressive-moving-average (ARMA) models seek to express a system function of a discretely sampled process as a rational function in the z-domain. Treating an ARMA model as a complex rational function, we discuss a metric defined on the set of complex rational functions. We give a natural measure of the “distance” between two ARMA processes. The paper concentrates on the mathematics behind the problem and shows that the various algebraic structures endow the choice of metric with some interesting and remarkable properties, which we discuss. We suggest that the metric can be used in at least two circumstances: (i) in which we have signals arising from various models that are unknown (so we construct the distance matrix and perform cluster analysis) and (ii) where there are several possible models M_i, all of which are known, and we wish to find which of these is closest to an observed data sequence modeled as M     

Joint Source–Channel Codes for MIMO Block-Fading Channels

We consider transmission of a continuous amplitude source over an L-block Rayleigh-fading M_t x M_r multiple-input multiple-output (MIMO) channel when the channel state information is only available at the receiver. Since the channel is not ergodic, Shannon's source-channel separation theorem becomes obsolete and the optimal performance requires a joint source-channel approach. Our goal is to minimize the expected end-to-end distortion, particularly in the high signal-to-noise ratio (SNR) regime. The figure of merit is the distortion exponent, defined as the exponential decay rate of the expected distortion with increasing SNR. We provide an upper bound and lower bounds for the distortion exponent with respect to the bandwidth ratio among the channel and source bandwidths. For the lower bounds, we analyze three different strategies based on layered source coding concatenated with progressive superposition or hybrid digital/analog transmission. In each case, by adjusting the system parameters we optimize the distortion exponent as a function of the bandwidth ratio. We prove that the distortion exponent upper bound can be achieved when the channel has only one degree of freedom, that is L = 1, and min{M_t ,M_r} =1. When we have more degrees of freedom, our achievable distortion exponents meet the upper bound for only certain ranges of the bandwidth ratio. We demonstrate that our results, which were derived for a complex Gaussian source, can be extended to more general source distributions as well.     

CRLB for DOA Estimation in Gaussian and Non-Gaussian Mixed Environments

The determination of Cramer-Rao lower bound (CRLB) as an optimality criterion for the problem of Direction-of-arrival (DOA) estimation is a very important issue. Several CRLBs on DOA estimation have been derived for Gaussian noise. However, a practical channel is affected by not only Gaussian background noise but also non-Gaussian noise such as impulsive interference. This paper derives the deterministic CRLB for Gaussian and non-Gaussian mixed environments. Since non-parametric kernel method is used to build the probability density function (PDF) of non-Gaussian noise, the CRLB derived is suitable for various noise distributions with or without symmetric PDF. The relationship between the CRLB for Gaussian noise and the proposed CRLB is also investigated. Theoretical analysis shows that the proposed CRLB provides a unified representation for both the cases of Gaussian and mixed environments. Computer simulations are included to verify the derived CRLB in different noise environments.     

Path map symbol release rules and the exponential metric tree[source coding]

To design a tree coder for source coding with a fidelity criterion, one must choose a suitable code generator, an efficient tree search algorithm, an appropriate distortion measure, and a path map symbol release rule. The performance of several path map symbol release rules when used with exhaustive searching of the exponential metric tree is investigated. The average single-letter distortion of fixed-length symbol release rules and two variable-length symbol release rules are derived for shallow search depths and compared to simulation results. The incremental or single-symbol release rule is shown to yield the best performance     

一种基于最小可察觉失真的立体图像质量客观评价方法

立体图像质量是评价立体视频系统性能的有效途径,而如何利用人类视觉特性对立体图像质量进行有效的评价是目前的研究难点。本文通过分析最小可察觉失真(JND,just noticeable distortion)视觉感知模型,并结合反映图像结构信息的奇异值矢量,提出了一种基于JND的立体图像质量客观评价方法。评价方法由图像质量评价和深度感知评价两部分组成,首先提取反映图像质量和深度感知的特征信息作为立体图像特征信息,然后根据立体图像的不同失真类型情况对其特征进行融合,通过支持向量回归(SVR,support vector Regression)预测得出立体图像质量的客观评价值。实验结果表明,采用本文提出的客观评价方法对立体数据测试库进行评价,在不同失真类型或混合失真评价结果中,Pearson线性相关系数(CC)值均在0.94以上,Spearman等级相关系数(SROCC)值均在0.92以上,符合人眼视觉特性,能够很好地预测人眼对立体图像的主观感知。     

SSIM-based distortion metric for film grain noise in HEVC

In video coding, the sum of squared differences (SSD) is traditionally used for rate-distortion optimization (RDO). However, SSD has been known that has low correlation on subjective quality. In particular, film grain noise (FGN)-synthesized video sequence is a very good example of subjective quality degradation with SSD-based RDO. Therefore, structural similarity (SSIM) has been considered for RDO owing to its simplicity and high correlation with subjective quality. The SSIM metric was not designed to be used for previous RDO framework; additional processing, such as content analysis or adaptive Lagrangian multipliers, was required in previous studies. Based on analyzing cases of degradation in SSIM-based coding, this study proposes a novel SSIM-like distortion measure. In this paper, two objectives are considered. First one is FGN-synthesized video coding using the SSIM-like distortion measure to preserve noise pattern. Seconds, the proposed metric is designed for direct application in previously developed RDO frameworks without scene-analysis-based RDO. The experimental results demonstrate that the proposed method reduces erroneous prediction blocks and the Bjøntegaard delta rate by 67.46% on average compared to original SSIM-based RDO for FGN-synthesized video sequences. The results show the proposed metric is effective for film grain noise in similar bit rate, compared to a high-efficiency video coding test model (HM16.6) and the original SSIM metric.     

Efficient no-reference metric for sharpness mismatch artifact between stereoscopic views

This paper analyzes sharpness mismatch between stereoscopic views. Sharpness mismatch is a special binocular mismatch and can occur through e.g. focus mismatch between stereoscopic cameras, errors in post-processing or asymmetric coding for low-bandwidth transmission, where one view is subsampled or transmitted at a much lower rate. Although blurred edges in one view can be suppressed by the corresponding sharper edges in the other view according to the binocular suppression phenomenon, sharpness mismatch can still be perceived and cause eye strain for viewers. Subjective studies were carried out with a test video dataset, in which the stereoscopic views are asymmetrically blurred by Gaussian low-pass filters since defocus-based effects of lens aberrations can be modeled as Gaussian blur. Also, an efficient novel automatic no-reference approach to measure the probability of sharpness mismatch is presented in this paper. The sharpness mismatch score is estimated by measuring width deviations of edge pairs in each “edge-significant” depth plane based on depth edges in both views. The probability of sharpness mismatch (PSM) is then calculated considering the perceptibility of edge width deviations considering absolute depth at which the edges occur. This PSM metric is evaluated using the test video dataset and blurriness dataset of LIVE 3D Phase II database. The experimental results show that the proposed metric outperforms the state-of-the-art stereo 3D quality metrics on analyzing sharpness mismatch between stereoscopic views.     

On-line estimation of hidden Markov model parameters based on theKullback-Leibler information measure

Sequential or online hidden Markov model (HMM) signal processing schemes are derived, and their performance is illustrated by simulation. The online algorithms are sequential expectation maximization (EM) schemes and are derived by using stochastic approximations to maximize the Kullback-Leibler information measure. The schemes can be implemented either as filters or fixed-lag or sawtooth-lag smoothers. They yield estimates of the HMM parameters including transition probabilities, Markov state levels, and noise variance. In contrast to the offline EM algorithm (Baum-Welch scheme), which uses the fixed-interval forward-backward scheme, the online schemes have significantly reduced memory requirements and improved convergence, and they can estimate HMM parameters that vary slowly with time or undergo infrequent jump changes. Similar techniques are used to derive online schemes for extracting finite-state Markov chains imbedded in a mixture of white Gaussian noise (WGN) and deterministic signals of known functional form with unknown parameters     

A no-reference sharpness metric based on the notion of relative blur for Gaussian blurred image

This work presents a no-reference sharpness metric for Gaussian blurred image. The metric is based on the notion of relative blur. The key concept is that the judgement on the sharpness closely relates to the degree of convenience for recognizing image objects on a certain scale. Based on this concept, the proposed metric is defined as relative blur with respect to certain object scale using an absolute blur measure. The object scale is characterized by a granularity analysis of image content. And the absolute blur is built on an analysis of edge local gray level distribution. The performance of the metric is tested and compared with some outstanding existing metrics in this field on three widely used databases. The experiment results show that the proposed metric can predict the sharpness of images in varying databases with high accuracy and reliability.     

Minimum-Error-Based Approximation Model for Symmetric Alpha Stable Distribution

In many communication channels the impulsive noise is usually assumed to be of a symmetric alpha stable (SαS) distribution. Unfortunately, except for the Gaussian, Cauchy, and Lévy laws, the analytical expressions for the probability density functions (PDF) of alpha stable distributions are unknown, resulting in very limited application of this distribution. In a practical system, the bi-parameter Cauchy–Gaussian mixture (BCGM) distribution is used to approximate the PDF of the SαS distribution to tackle this difficulty. In this paper, we derive the optimal mixture ratio of the BCGM model based on the minimum square error criterion and furthermore propose a simplified and robust version of BCGM for the SαS distribution. Numerical simulations show that our proposed model achieves better performance and is more robust than the conventional models, without incurring additional complexity.     

Information rates of non-Gaussian processes

The rate distortion functionR(D)of an information source was introduced by Shannon to specify the channel capacity required in transmitting information from the source with an average distortion not exceedingD. Exact rates have been calculated for Gaussian sources under a mean-square error criterion. For non-Gaussian continuous sources, Shannon has given upper and lower bounds onR(D). In specific cases, the difference between these two bounds may not be sufficiently small to provide a useful estimate ofR(D). The present paper is concerned with improving estimates of information rates of non-Gaussian sources under a mean-square error criterion. The sources considered are ergodic, and their statistical properties are characterized by a bounded and continuousn-dimensional probability density function. The paper gives a set of necessary and sufficient conditions forR(D)to equal Shannon's lower bound. For sources satisfying these conditions, exact rate calculations are possible. For sources that do not satisfy the required conditions, an improved upper bound is obtained that never exceeds Shannon's upper bound. Under rather general conditions, the new upper bound approaches Shannon's lower bound for small values of distortion, so that the true value ofR(D)can be estimated very accurately for smallD.     

Vision-model-based impairment metric to evaluate blocking artifactsin digital video

In this paper investigations are conducted to simplify and refine a vision-model-based video quality metric without compromising its prediction accuracy. Unlike other vision-model-based quality metrics, the proposed metric is parameterized using subjective quality assessment data recently provided by the Video Quality Experts Group. The quality metric is able to generate a perceptual distortion map for each and every video frame. A perceptual blocking distortion metric (PBDM) is introduced which utilizes this simplified quality metric. The PBDM is formulated based on the observation that blocking artifacts are noticeable only in certain regions of a picture. A method to segment blocking dominant regions is devised, and perceptual distortions in these regions are summed up to form an objective measure of blocking artifacts. Subjective and objective tests are conducted and the performance of the PBDM is assessed by a number of measures such as the Spearman rank-order correlation, the Pearson correlation, and the average absolute error The results show a strong correlation between the objective blocking ratings and the mean opinion scores on blocking artifacts     

The Gaussian Transform of Distributions: Definition, Computation and Application

This paper introduces the general-purpose Gaussian transform of distributions, which aims at representing a generic symmetric distribution as an infinite mixture of Gaussian distributions. We start by the mathematical formulation of the problem and continue with the investigation of the conditions of existence of such a transform. Our analysis leads to the derivation of analytical and numerical tools for the computation of the Gaussian transform, mainly based on the Laplace and Fourier transforms, as well as of the afferent properties set (e.g., the transform of sums of independent variables). The Gaussian transform of distributions is then analytically derived for the Gaussian and Laplacian distributions, and obtained numerically for the generalized Gaussian and the generalized Cauchy distribution families. In order to illustrate the usage of the proposed transform we further show how an infinite mixture of Gaussians model can be used to estimate/denoise non-Gaussian data with linear estimators based on the Wiener filter. The decomposition of the data into Gaussian components is straightforwardly computed with the Gaussian transform, previously derived. The estimation is then based on a two-step procedure: the first step consists of variance estimation, and the second step consists of data estimation through Wiener filtering. To this purpose, we propose new generic variance estimators based on the infinite mixture of Gaussians prior. It is shown that the proposed estimators compare favorably in terms of distortion with the shrinkage denoising technique and that the distortion lower bound under this framework is lower than the classical minimum mean-square error bound.     

Music Analysis Using Hidden Markov Mixture Models

We develop a hidden Markov mixture model based on a Dirichlet process (DP) prior, for representation of the statistics of sequential data for which a single hidden Markov model (HMM) may not be sufficient. The DP prior has an intrinsic clustering property that encourages parameter sharing, and this naturally reveals the proper number of mixture components. The evaluation of posterior distributions for all model parameters is achieved in two ways: 1) via a rigorous Markov chain Monte Carlo method; and 2) approximately and efficiently via a variational Bayes formulation. Using DP HMM mixture models in a Bayesian setting, we propose a novel scheme for music analysis, highlighting the effectiveness of the DP HMM mixture model. Music is treated as a time-series data sequence and each music piece is represented as a mixture of HMMs. We approximate the similarity of two music pieces by computing the distance between the associated HMM mixtures. Experimental results are presented for synthesized sequential data and from classical music clips. Music similarities computed using DP HMM mixture modeling are compared to those computed from Gaussian mixture modeling, for which the mixture modeling is also performed using DP. The results show that the performance of DP HMM mixture modeling exceeds that of the DP Gaussian mixture modeling.     

Optimal error exponents in hidden Markov models order estimation

We consider the estimation of the number of hidden states (the order) of a discrete-time finite-alphabet hidden Markov model (HMM). The estimators we investigate are related to code-based order estimators: penalized maximum-likelihood (ML) estimators and penalized versions of the mixture estimator introduced by Liu and Narayan (1994). We prove strong consistency of those estimators without assuming any a priori upper bound on the order and smaller penalties than previous works. We prove a version of Stein's lemma for HMM order estimation and derive an upper bound on underestimation exponents. Then we prove that this upper bound can be achieved by the penalized ML estimator and by the penalized mixture estimator. The proof of the latter result gets around the elusive nature of the ML in HMM by resorting to large-deviation techniques for empirical processes. Finally, we prove that for any consistent HMM order estimator, for most HMM, the overestimation exponent is .