A Modified Iterative Alternating Direction Minimization Algorithm for Impulse Noise Removal in Images

National Natural Science Foundation of China [61302174, 61201045]; Scientific Research Foundation for the Introduction of Talent at Xiamen University of Technology [YKJ12021R]; Key Lab of Digital Signal and Image Processing of Guang dong Province [2013GDDSIPL-07, 54600321]; Fundamental Research Funds for the Central Universities [2013SH002]; Natural Science Foundation of Shaanxi Province of China [2013JM8015]Images are often corrupted by impulse noise. In this paper, an alternating direction minimization with continuation algorithm is modified and iteratively used to remove the impulse noise in images by exploring its self-similarity. A patch-based nonlocal operator and sparse representation are married in the l(1)-l(1) optimization model to be solved. Simulation results demonstrate that the proposed algorithm outperforms typical denoising methods in terms of preserving edges and textures for both salt-and-pepper noise and random-valued impulse noise. It can be also applied to suppress impulse noise-like artifacts in real mural images