Hooke and Jeeves algorithm for linear least-square problems in sparse signal reconstruction

Greedy algorithms are the major algorithmic approaches to sparse signal reconstruction from an incomplete set of linear measurements. All the greedy algorithms involve solving linear least-square problems. This is usually implemented via CGLS. Though CGLS uses a fixed number of iterations, experiments confirm that CGLS costs more than 50 percent of the total running time of greedy algorithms. In order to reduce the running time, we introduce a method called HJLS, which applies Hooke and Jeeves algorithm to solve the least-square problems. As the columns of the measurement matrix are nearly orthogonal, HJLS also converges in a fixed number of iterations. Comparative experiments between HJLS and CGLS show that the number of iterations used in HJLS is fewer and implementing HJLS instead of CGLS reduces the total running time of greedy algorithms by more than 20 percent.