Fast iteratively reweighted least squares for lp regularized image deconvolution and reconstruction

Iteratively reweighted least squares (IRLS) is one of the most effective methods to minimize the lp regularized linear inverse problem. Unfortunately, the regularizer is nonsmooth and nonconvex when 0 < p < 1. In spite of its properties and mainly due to its high computation cost, IRLS is not widely used in image deconvolution and reconstruction. In this paper, we first derive the IRLS method from the perspective of majorization minimization and then propose an Alternating Direction Method of Multipliers (ADMM) to solve the reweighted linear equations. Interestingly, the resulting algorithm has a shrinkage operator that pushes each component to zero in a multiplicative fashion. Experimental results on both image deconvolution and reconstruction demonstrate that the proposed method outperforms state-of-the-art algorithms in terms of speed and recovery quality.