A complementary matching pursuit algorithm for sparse approximation

This paper introduces the concept of a complementary matching pursuit for sparse approximation. The algorithm is analogous to the classical matching pursuit but done in the row-space of the dictionary matrix. A deeper analysis of the algorithm shows that the residual error at any iteration may not be orthogonal to the immediately selected atom, however, this brings about the possibility of increasing the convergence speed and improving the sparsity of the solution vector. This is validated through simulations with a random dictionary created using the K-SVD algorithm.