Blind Separation of complex-valued mixtures: Sparse representation in polar and cartesian scatter-plots

This study is concerned with reconstruction of complex-valued components comprising a linear mixing model of unknown real-valued sources, given a set of their complex-valued mixtures. We adopt previous results in the area of Blind Source Separation (BSS) of linear mixtures, based on sparse representation by means of a multiscale framework such as wavelet packets, and exploit the properties of sparse representation obtained by projection onto a proper space. We propose two techniques, developed for dealing with complex-valued mixtures of real sources and incorporate sparsity-dependent clustering via projection onto a proper space; one onto polar coordinates, and the other onto cartesian coordinates. We describe various aspects of the proposed techniques, and present an experiment of noisy mixtures of images.