Istituto di Scienza e Tecnologie dell'Informazione     
Tonazzini A., Bedini L., Kuruoglu E. E., Salerno E. Bind separation of time-correlated sources from noisy data. Technical report, 2001.
This paper deals with the blind separation and reconstruction of source signals from their mixtures with unknown coefficients, in the practical case where some amount of noise affects the mixtures themselves. We address the blind source separation problem within the ICA approach, i.e. assuming the statistical independence of the source signals, and reformulate it in a Bayesian estimation framework. In this way, the flexibility of the Bayesian formulation in accounting for available knowledge we may possess about the original signals can be exploited to describe time correlation of the single sources, through the use of suitable Gibbs priors. We propose a MAP estimation method and derive the theoretical formulation of two algorithms to recover both the mixing matrix and the sources: the first is based on the Expectation-Maximization technique and the mean field approximation; the second is based on alternating maximization within a simulated annealing scheme. We verified that, under the adopted approximations, the two algorithms are substantially equivalent. Thus, we experimented the alternating maximization scheme on one dimensional synthetic signals and found that a source model accounting for time correlation is able to increase robustness against noise.
Subject Blind Source Separation, Independent Component Analysis, MarkovRandom Fields, Bayesian Estimation, Expectation-Maximization, SimulatedAnnealing.
I.4.5 [Image Processing and Computer Vision]: Reconstruction
G.3 [Probability and Statistics]: Probabilistic algorithms (includingMonte Carlo)
I.2.6 [Artificial Intelligence]: Learning: Parameter learning.
62M40 Statistics [Inference from stochastic processes] Random fields
image analysis.

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