A nonconvex penalization algorithm with automatic choice of the regularization parameter in sparse imaging

Abstract

This paper introduces an efficient method for solving nonconvex penalized minimization problems. The topic is relevant in many imaging problems characterized by sparse data. The proposed method originates from the iterative reweighting l1 scheme, modified by the automatic update of the regularization parameter on the basis of the behavior of the objective function. Besides proving the convergence of the method, a modified algorithm is obtained and the performance is tested on two different sparse imaging problems. The proposed method can be viewed as a general framework which can be adapted to different one-parameter nonconvex penalty functions and applied to problems characterized by sparse data.