Low rank prior and l0 norm to remove impulse noise in images

Patch-based low rank is an important prior assumption for image processing. Moreover, according to our calculation, the optimization of l0 norm corresponds to the maximum likelihood estimation under random-valued impulse noise. In this article, we thus combine exact rank and l0 norm for removing the noise. It is solved formally using the alternating direction method of multipliers (ADMM), with our previous patch-based weighted filter (PWMF) producing initial images. Since this model is not convex, we consider it as a Plug-and-Play ADMM, and do not discuss theoretical convergence properties. Experiments show that this method has very good performance, especially for weak or medium contrast images.