Deblurring Poisson noisy images by total variation with overlapping group sparsity

• Published in: Applied mathematics and computation Vol. 289; pp. 132 - 148
• Main Authors: Lv, Xiao-Guang, Jiang, Le, Liu, Jun
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 20.10.2016
• Subjects: Alternating direction method of multipliers; Deblurring; Overlapping group sparsity; Poisson noise; Total variation; Deblurring; Total variation; Alternating direction method of multipliers; Overlapping group sparsity; Poisson noise
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2016.03.029

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.