Abstract: This paper addresses the problem of summarizing the posterior distributions that typically arise, in a Bayesian framework, when dealing with signal decomposition problems with unknown number of components. Such posterior distributions are defined over union of subspaces of differing dimensionality and can be sampled from using modern Monte Carlo techniques, for instance the increasingly popular RJ-MCMC method. No generic approach is available, however, to summarize the resulting variable-dimensional samples and extract from them component-specific parameters. We propose a novel approach to this problem, which consists in approximating the complex posterior of interest by a "simple"---but still variable-dimensional---parametric distribution. The distance between the two distributions is measured using the Kullback-Leibler divergence, and a Stochastic EM-type algorithm, driven by the RJ-MCMC sampler, is proposed to estimate the parameters. The proposed algorithm is illustrated on the fundamental signal processing example of joint detection and estimation of sinusoids in white Gaussian noise.
Abstract: This paper addresses the behavior in low SNR situations of the algorithm proposed by Andrieu and Doucet (IEEE T. Signal Proces., 47(10), 1999) for the joint Bayesian model selection and estimation of sinusoids in Gaussian white noise. It is shown that the value of a certain hyperparameter, claimed to be weakly influential in the original paper, becomes in fact quite important in this context. This robustness issue is fixed by a suitable modification of the prior distribution, based on model selection considerations. Numerical experiments show that the resulting algorithm is more robust to the value of its hyperparameters.
Abstract: Retinal images acquired using a fundus camera often contain low grey, low level contrast and are of low dynamic range. This may seriously affect the automatic segmentation stage and subsequent results; hence, it is necessary to carry-out preprocessing to improve image contrast results before segmentation. Here we present a new multi-scale method for retinal image contrast enhancement using Contourlet transform. In this paper, a combination of feature extraction approach which utilizes Local Binary Pattern (LBP), morphological method and spatial image processing is proposed for segmenting the retinal blood vessels in optic fundus images. Furthermore, performance of Adaptive Neuro-Fuzzy Inference System (ANFIS) and Multilayer Perceptron (MLP) is investigated in the classification section. The performance of the proposed algorithm is tested on the publicly available DRIVE database. The results are numerically assessed for different proposed algorithms.
Abstract: Reversible jump MCMC (RJ-MCMC) sampling techniques, which allow to jointly tackle model selection and parameter estimation problems in a coherent Bayesian framework, have become increasingly popular in the signal processing literature since the seminal paper of Andrieu and Doucet (IEEE Trans. Signal Process., 47(10), 1999). Crucial to the implementation of any RJ-MCMC sampler is the computation of the so-called Metropolis-Hastings-Green (MHG) ratio, which determines the acceptance probability for the proposed moves.
This note discusses the computation of the MHG ratio, in the case where the proposal kernel can be decomposed as a mixture of simpler kernels, for which the MHG ratio is easy to compute. We provide sufficient conditions under which the MHG ratio of the mixture can be deduced from the MHG ratios of the elementary kernels of which it is composed.
As an application, we consider the case of Birth-or-Death moves---the simplest kind of trans-dimensional move, which is used in virtually all applications of RJ-MCMC to signal decomposition problems. It turns out that the expression of the MHG ratio that was given in the paper of Andrieu and Doucet was erroneous. Unfortunately, this mistake has contaminated most subsequent papers dealing with RJ-MCMC sampling in the signal processing literature.
Abstract: This thesis addresses the challenges encountered when dealing with signal decomposition problems with an unknown number of components in a Bayesian framework. Particularly, we focus on the issue of summarizing the variable-dimensional posterior distributions that typically arise in such problems. Such posterior distributions are defined over union of subspaces of differing dimensionality, and can be sampled from using modern Monte Carlo techniques, for instance the increasingly popular Reversible-Jump MCMC (RJ-MCMC) sampler. No generic approach is available, however, to summarize the resulting variable-dimensional samples and extract from them component-specific parameters. One of the main challenges that needs to be addressed to this end is the label-switching issue, which is caused by the invariance of the posterior distribution to the permutation of the components.
We propose a novel approach to this problem, which consists in approximating the complex posterior of interest by a âsimpleââbut still variable-dimensional parametric distribution. We develop stochastic EM-type algorithms, driven by the RJ-MCMC sampler, to estimate the parameters of the model through the minimization of a divergence measure between the two distributions. Two signal decomposition problems are considered, to show the capability of the proposed approach both for relabeling and for summarizing variable dimensional posterior distributions: the classical problem of detecting and estimating sinusoids in white Gaussian noise on the one hand, and a particle counting problem motivated by the Pierre Auger project in astrophysics on the other hand.
