Wavelet domain blind image separation

Abstract

In this work, we consider the problem of blind source separation in the wavelet domain via a Bayesian estimation framework. We use the sparsity and multiresolution properties of the wavelet coefficients to model their distribution by heavy tailed prior probability laws: the generalized exponential family and the Gaussian mixture family. Appropriate MCMC algorithms are developped in each case for the estimation purposes and simulation results are presented for comparaison.

Bayesian approaches

“…Among the most common source models is the Generalized Gaussian (GG) [70,75,28], gamma distribution [49] and mixture of Gaussians (MoG) [75,64,28,27,29]. To be able to separate sources, it is important that each source differs from the other in some respect.…”

A Hierarchical Bayesian Model for Frame Representation

“…Hybrid MCMC algorithms [24,25] are designed combining Metropolis-Hastings (MH) [26] and Gibbs [27] moves to sample according to the posterior distribution of interest. MCMC algorithms and WT have been jointly investigated in some works dealing with signal denoising in a Bayesian framework [18,[28][29][30]. However, in contrast with the present work where overcomplete frame representations are considered, these works are limited to wavelet bases for which the hyper-parameter estimation problem is much easier to handle.…”

“…In addition, the proposed method can be applied to noisy data when imprecise measurements of the signal are only available. Our work takes advantage of the current developments in Markov Chain Monte Carlo (MCMC) algorithms [15][16][17] that have already been investigated for instance in image separation [18], image restoration [19] and brain activity detection in functional MRI [20,21]. These algorithms have also been investigated for signal/image processing problems with sparsity constraints.…”

Blind Image Separation using Sparse Representation

“…Recently, an important research activity has been observed for solving the BSS problem using a sparse representation of the source signals. Solutions for the blind separation of image sources using sparsity include the wavelet-transform domain methods in [6][7][8] and the method in [9] using projection onto sparse dictionaries. In this work, we propose a new solution based on the transformed image sparsity.…”