A comparative study of some greedy pursuit algorithms for sparse approximation

Solving an under-determined system of equations for the sparsest solution has attracted considerable attention in recent years. Among the two well known approaches, the greedy algorithms like matching pursuits (MP) are simpler to implement and can produce satisfactory results under certain conditions. In this paper, we compare several greedy algorithms in terms of the sparsity of the solution vector and the approximation accuracy. We present two new greedy algorithms based on the recently proposed complementary matching pursuit (CMP) and the sensing dictionary framework, and compare them with the classical MP, CMP, and the sensing dictionary approach. It is shown that in the noise-free case, the complementary matching pursuit algorithm performs the best among these algorithms.