Abstract: In image restoration, images are often assumed to be sparse after taking gradient. Nonconvex regularizers could produce more sparse gradients than convex regularizers. In this paper, based on some recent nonconvex regularizers, we propose several nonconvex models for image deblurring under Poisson noise. We develop efficient numerical algorithms for solving the proposed models and carry out the convergence analysis. Numerical results show that the proposed models achieve an enhanced gradient sparsity and yield restoration results competitive with some existing methods.

Key words: nonconvex regularization, alternating direction method of multipliers, sparsity, Poisson noise, image deblurring