Improved iteratively reweighted least squares algorithms for sparse recovery problem

In this paper, some new algorithms based on the iteratively reweighted least squares (IRLS) method are proposed for sparse recovery problem. There are two important parameters in the IRLS method: a weighted parameter and a regularization parameter. On the one hand, in order to improve the performance of IRLS method, a new way is given to update the weight vector. On the other hand, for the regularization parameter, three new update methods are introduced to avoid the phenomenon that the regularization parameter drops too fast. Then, some improved iteratively reweighted least squares (IIRLS) algorithms are proposed, and their convergence and convergence rate are analyzed. The local convergence of our algorithms is superlinear and approaches a quadratic rate in special cases. Finally, a large number of algorithms are compared in solving the sparse recovery problem, including IRLS methods and IIRLS methods with different weighting parameters and regularization parameters, and certain iterative methods. The experimental results demonstrate that the proposed methods are efficient and promising.