A Two-Level Simultaneous Orthogonal Matching Pursuit Algorithm for Simultaneous Sparse Approximation Problems

In this paper, we propose a two-level simultaneous orthogonal matching pursuit (TLSOMP) algorithm for simultaneous sparse approximation (SSA) problems. Most existing algorithms for SSA problems are directly generalized from the ones for the sparse approximation (SA) problems, for example, the simultaneous orthogonal matching pursuit (SOMP) method is generalized from the orthogonal matching pursuit (OMP) method. Our newly proposed algorithm is designed from another view-point. We first analyze the noiseless case and propose a selection algorithm. Motivated by the analysis and presuming noise as a perturbation, we extend the selection algorithm into a TLSOMP algorithm. This novel algorithm mainly uses the information from the subspace spanned by the multiple signals, which is not available in SA problems. Numerical experiments show the superiority of our TLSOMP algorithm over other traditional SSA solvers.