An efficient non-convex total variation approach for image deblurring and denoising.

Total variation (TV) is broadly utilized in image processing because it is able to preserve sharp edges and object boundaries, which are usually the most important parts of an image. Recently, the non-convex functions such as the smoothly clipped absolute deviation, the minimax concave penalty, the capped ℓ 1 -norm penalty and the ℓ p quasi-norm with 0 < p < 1 have been shown remarkable advantages in sparse learning due to the fact that they can overcome the over-penalization associated with the ℓ 1 -norm. In this paper, an efficient non-convex total variation approach for image deblurring and denoising model has been proposed, which combines a non-convex regularization term and a non-convex data fitting term perfectly. Firstly, the non-convex functions are employed into the regularization term and the fidelity term for enhancing the sensitivity to sharp edges and object boundaries. Secondly, the optimizing minimization method based on the alternating direction method of multipliers (ADMM) is proposed to solve the non-convex total variation optimization problem. The resulting subproblems either have closed-form solutions or can be solved by fast solvers, which makes the ADMM particularly efficient. In theory, with the help of the smoothing technique and Kurdyka-Lojasiewicz function, we prove that the sequence generated by the ADMM converges to a stationary point when the penalty parameter is above a computable threshold. The numerical experiments illustrate that our proposed non-convex total variation model outperforms the existing convex and non-convex total variation models. [ABSTRACT FROM AUTHOR]