An improvement of the penalty decomposition method for sparse approximation

The Penalty Decomposition (PD) method is an effective and versatile algorithm for sparse optimization, which has been used in different applications. The PD method may be slow, since it needs to solve many subproblems. The accelerated iteration hard thresholding (AIHT) method is also a powerful method for sparse optimization, but has a main drawback that it requires a prior estimation of the sparsity level. In this paper, an improvement of the penalty decomposition method is proposed for the sparse optimization problem, which embeds the AIHT method into the PD method. The proposed method has the advantages of the PD method and the AIHT method, but avoids their disadvantages. The convergence analysis of the proposed method is given as well. Moreover, computational experiments on a number of test instances demonstrate the effectiveness of the proposed method in accurately generating sparse and redundant representations of one-dimensional random signals and two-dimensional CT images.