Sparse approximation with an orthogonal complementary matching pursuit algorithm

This paper presents the orthogonal extension of the recently introduced complementary matching pursuit (CMP) algorithm for sparse approximation. The CMP algorithm is analogous to the matching pursuit (MP) but done in the row-space of the dictionary matrix. It suffers from a similar sub-optimality as the MP. The orthogonal complementary matching pursuit algorithm (OCMP) presented here tries to remove this sub-optimality by updating the coefficients of all selected atoms at each iteration. Its development from the CMP follows the same procedure as of the orthogonal matching pursuit (OMP). In contrast with OMP, the residual errors resulting from the OCMP may not be orthogonal to all the atoms selected up to the respective iteration. Though the residual energy may increase over the OMP during the first iterations, it is shown that, compared with OMP, the convergence speed is increased in the subsequent iterations and the sparsity of the solution vector is improved.