Poisson image restoration using a novel directional TVp regularization

• DOI: 10.1016/j.sigpro.2021.108407
• Publication Date: 2021-11-23T17:08:48Z
• Authors: Jun Zhang; Pengcheng Li; Junci Yang; Mingxi Ma; Chengzhi Deng
• Keywords: 0101 mathematics; 01 natural sciences

Abstract The degree of Poisson noise depends on the image intensity, which makes Poisson image restoration very challenging. Moreover, complex structures of images desire suitable regularizations to describe. In this paper, we propose a new image restoration model under Poisson noise based on an adaptive weighted directional T V p regularization. The rotation matrix can keep the diffusion of the corresponding Euler-Lagrange equation along with the tangential direction of the edge, and the adaptive weighted matrix can enhance the diffusion. Owing to its adaptivity, our proposed model can simultaneously handle several dominant directions. Besides, the l p -quasinorm regularization promotes the image sparsity. To solve it efficiently, we design an alternating direction method of multipliers (ADMM). The related l 2 − l p subproblem is solved by using the half-quadratic algorithm with guaranteed convergence. Experimental results on natural and synthetic images show the effectiveness of the proposed method over the state-of-the-art variational methods.