A pseudo-heuristic parameter selection rule for l1-regularized minimization problems

This paper considers the regularization parameter determination of l1-regularized minimization problem. We solve the l1-regularized problem using iterative reweighted least squares (IRLS) which involves solving a linear system whose coefficient matrix has the form αM+(1−α)N (α∈(0,1)). The aim of this paper is to find an efficient and computationally inexpensive algorithm to both choose the regularization parameter and solve the l1-regularized problem. In order to achieve this, we propose an IRLS algorithm with adaptive regularization parameter selection based on a heuristic parameter determination rule-de Boor's parameter selection criterion. Compared with some of the state-of-the-art algorithms and parameter selection rules, the numerical experiments show the efficiency and robustness of the proposed method.