In this paper, we consider the problem of blind signal and image separation
using a sparse representation of the images in the wavelet domain. We consider
the problem in a Bayesian estimation framework using the fact that the
distribution of the wavelet coefficients of real world images can naturally be
modeled by an exponential power probability density function. The Bayesian
approach which has been used with success in blind source separation gives also
the possibility of including any prior information we may have on the mixing
matrix elements as well as on the hyperparameters (parameters of the prior laws
of the noise and the sources). We consider two cases: first the case where the
wavelet coefficients are assumed to be i.i.d. and second the case where we
model the correlation between the coefficients of two adjacent scales by a
first order Markov chain. This paper only reports on the first case, the second
case results will be reported in a near future. The estimation computations are
done via a Monte Carlo Markov Chain (MCMC) procedure. Some simulations show the
performances of the proposed method. Keywords: Blind source separation,
wavelets, Bayesian estimation, MCMC Hasting-Metropolis algorithm.Comment: Presented at MaxEnt2002, the 22nd International Workshop on Bayesian
and Maximum Entropy methods (Aug. 3-9, 2002, Moscow, Idaho, USA). To appear
in Proceedings of American Institute of Physic
