Deblurring Poisson noisy images by total variation with overlapping group sparsity

Deblurring Poisson noisy images has recently been subject of an increasingly amount of works in various applications such as astronomical imaging, fluorescent confocal microscopy imaging, single particle emission computed tomography (SPECT) and positron emission tomography (PET). Many works promote the introduction of an explicit prior on the solution to regularize the ill-posed inverse problem for improving the quality of the images. In this paper, we consider using the total variation with overlapping group sparsity as a prior information. The proposed method can avoid staircase effect and preserve edges in the restored images. After converting the proposed model to a constrained problem by variable splitting, we solve the corresponding problem with the alternating direction method of multipliers (ADMM). Numerical examples for deblurring Poisson noisy images are given to show that the proposed method outperforms some existing methods in terms of the signal-to-noise ratio, relative error and structural similarity index.