Cyclic Sparse Greedy Deconvolution

The purpose of this study is to introduce the concept of cyclic sparsity or cyclosparsity in deconvolution framework for signals that are jointly sparse and cyclostationary. Indeed, all related works in this area exploit only one property, either sparsity or cyclostationarity and never both properties together. Although, the key feature of the cyclosparsity concept is that it gathers both properties to better characterize this kind of signals. We show that deconvolution based on cyclic sparsity increases the performances and reduces significantly the computation cost. Finally, we use simulations to investigate the behavior in deconvolution framework of the algorithms MP, OMP and theirs respective extensions to cyclic sparsity context, Cyclo-MP and Cyclo-OMP.