Blind separation of mixed images using multiscale transforms

It was previously shown that sparse representations can improve and simplify the estimation of an unknown mixing matrix of a set of images and thereby improve the quality of separation of source images. Here we propose a multiscale approach to the problem of blind separation of images from a set of their mixtures. We take advantage of the properties of multiscale transforms such as wavelet packets and decompose signals and images according to sets of local features. The resulting partial representations on a tree of data structure depict various degrees of sparsity. We show how the separation error is affected by the sparsity of the decomposition coefficients, and by the misfit between the prior, formulated in accordance with the probabilistic model of the coefficients distribution, and the actual distribution of the coefficients. Our error estimator, based on the Taylor expansion of the quasi log-likelihood function, is used in selection of the best subsets of coefficients, utilized in turn for further separation. The performance of the proposed method is assessed by separation of noise-free and noisy data. Experiments with simulated and real signals and images demonstrate significant improvement of separation quality over previously reported results.