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Blind Separation of Reflections With Relative Spatial Shifts

We address the problem of blind separation of image mixtures (resulting, e.g., from reflections through window glass) consisting of pure unknown relative spatial-shifts in addition to scalar mixing coefficients. Most (and maybe all) existing approaches to the problem assume static mixtures, i.e., the spatial positions of the source images are assumed to remain fixed between snapshots. We propose an integrated method to estimate both the mixing coefficients and the spatial-shifts using a second-order statistics based algorithm, which uses specially parameterized approximate joint diagonalization of two-dimensional-spectra matrices. The accommodation of spatial shifts allows the exploitation of further diversity between snapshots, and thus enables to attain improved separation, especially when the static mixing coefficients are ill-conditioned - as we demonstrate using simulations results