A TV-log nonconvex approach for image deblurring with impulsive noise

•A TV-log nonconvex model for image deblurring with impulsive noise is proposed.•The new model can overcome the limitation of convex optimization model.•A difference of convex functions algorithm with adaptive proximal parameter is developed.•The sequence generated by the proposed algorithm converges to a critical point. In this paper, we study the image deblurring with impulsive noise problem. In order to find a high quality recovery solution, we propose a nonconvex optimization model that combines total variation regularization and nonconvex log penalty for data fitting. The new model can overcome the limitation of the L1-norm penalized data fitting term with total variation regularization model for high noise levels, and is easier to choose the scalar parameter in the data fitting term than the existing methods. For solving the nonconvex optimization problem, a difference of convex (DC) functions algorithm with adaptive proximal parameter is developed. Theoretically, using the Kurdyka-Łojasiewicz property, we establish that the sequence generated by the proposed algorithm converges to a critical point. The experiment results demonstrate the superiority of the new approach against the competing methods.