NONLINEAR

Sparse representation of information by decreasing the dimensionality of a data set without losing its information is a central aim of signal processing. Emerging non-linear techniques for signal representation achieve this goal by decomposing the signal as a superposition of elements, normally referred to as ‘atoms', selected from a large redundant set called a ‘dictionary'. The problem of finding the sparsest representation of a signal is, in general, intractable with classical computers. However, highly non-linear approximations have been proved to be very powerful, even when implemented by algorithms which do not seek the optimal solution with regard sparseness, but attempt to make tractable the problem of finding a sparse enough solution... This project focuses on the development of highly non-linear methods for sparse signal representation and disseminates the computational tools for their implementation. The proposed methods evolve by stepwise selection of atoms extending those..