The first part of this paper proposes a greedy pursuit algorithm, called simultaneous orthogonal matching pursuit (S-OMP), for simultaneous sparse approximation. Then it presents some numerical experiments that demonstrate how a sparse model for the input signals can be identified more reliably given several input signals. Afterward, the paper proves that the S-OMP algorithm can compute provably good solutions to several simultaneous sparse approximation problems.
The second part of the paper develops another algorithmic approach called convex relaxation, and it provides theoretical results on the performance of convex relaxation for simultaneous sparse approximation.