Beyond ICA: robust sparse signal representations

In many applications it is necessary to perform some decomposition of observed signals or data in such a way that components have some special properties or structures such as statistical independence, sparsity, smoothness, nonnegativity, prescribed statistical distributions and/or specific temporal structure. In this paper we discuss cost functions whose minimization solve such problems and we present new properties that characterize optimal solutions for sparse representations. Especially, we discuss robust cost functions in order to find sparse representation of noisy signals. Furthermore, we discuss sub-band decomposition preprocessing to relax independence conditions for source signals.