Hybrid priors based on weighted hyper-Laplacian with overlapping group sparsity for poisson noise removal

Poisson noise widely exists in photo-limited imaging systems, which is very difficult to remove because of its signal-dependent and multiplicative characteristics. In this paper, we propose a new hybrid regularizer variational model for removing Poisson noise. Based on the weighted hyper-Laplacian prior, the hybrid model combines the overlapping group sparse total variation with the high-order nonconvex total variation (HONTV) as a hybrid regularizer. The proposed model combines the advantages of the HONTV regularizer and the weighted hyper-Laplacian prior with overlapping group sparsity regularizer, it can more effectively preserve sharp edges and details while alleviating the staircase artifacts. To solve the non-convex and non-smooth model, we proposed an efficient alternating minimization method under the framework of alternating direction method of multipliers, where the majorization-minimization algorithm and generalized soft threshold algorithm are adopted to solve the corresponding subproblems. Numerical experiments show that the proposed method has higher quality image recovery than several existing methods.