Blind Separation methods based on correlation for sparse possibly-correlated images

In this paper, we propose Blind Source Separation (BSS) methods for possibly-correlated images, based on a low sparsity assumption. To satisfy this sparsity condition, one of the versions of our methods applies a wavelet transform to the observed images before performing separation. Another version directly operates in the original spatial domain, when the sources are sparse enough in this domain. Both methods consist in finding, in the considered sparse representation domain, tiny zones where only one source is active. The column of the mixing matrix corresponding to this source is then estimated in this zone. We also propose extensions of these methods, with automated selection of adequate analysis parameters. Various tests show the good performance of these approaches (SIR improvement often higher than 40 dB).