Sparse deconvolution by means of genetic algorithms

In sparse deconvolution two interrelated problems have to be addressed: detection of the peaks of a sparse signal and estimation of their amplitudes. The detection part is a highly nonlinear combinatory problem. Once a solution for the peak positions is obtained, their amplitudes can be estimated analytically. Based on genetic algorithms (powerful optimisation techniques inspired by Nature paradigms), we propose a method for sparse deconvolution in which spike detection is carried out following a genetic search, while amplitude estimation is performed by iteration methods which converge to the existing analytical solutions. Simulation results show the advantageous behaviour of our method, in comparison to a well-known sparse deconvolution approaches