A Two-Level Simultaneous Orthogonal Matching Pursuit Algorithm for Simultaneous Sparse Approximation Problems (CSIAM Transactions on Applied Mathematics, 2023)
In this paper, we propose a two-level simultaneous orthogonal matchingpursuit (TLSOMP) algorithm for simultaneous sparse approximation (SSA) problems.Most existing algorithms for SSA problems are directly generalized from the ones forthe sparse approximation (SA) problems, for example, the simultaneous orthogonalmatching pursuit (SOMP) method is generalized from the orthogonal matching pursuit (OMP) method. Our newly proposed algorithm is designed from another viewpoint. We first analyze the noiseless case and propose a selection algorithm. Motivatedby the analysis and presuming noise as a perturbation, we extend the selection algorithm into a TLSOMP algorithm. This novel algorithm mainly uses the informationfrom the subspace spanned by the multiple signals, which is not available in SA problems. Numerical experiments show the superiority of our TLSOMP algorithm overother traditional SSA solvers.
Keywords: Simultaneous sparse approximation; two-level simultaneous orthogonal matching pursuit; subspace approximation.