Proximal Linearized Minimization Algorithm for Nonsmooth Nonconvex Minimization Problems in Image Deblurring with Impulse Noise

Impulse noise removal is an important task in image restoration. In this paper, we introduce a general nonsmooth nonconvex model for recovering images degraded by blur and impulsive noise, which can easily include some prior information, such as box constraint or low rank, etc. To deal with the nonconvex problem, we employ the proximal linearized minimization algorithm. For the subproblem, we use the alternating direction method of multipliers to solve it. Furthermore, based on the assumption that the objective function satisfies the KurdykaLojasiewicz property, we prove the global convergence of the proposed algorithm. Numerical experiments demonstrate that our method outperforms both the l1TV and Nonconvex TV models in terms of subjective and objective quality measurements.