Image restoration and reconstruction by non-convex total variation and shearlet regularizations

The total variation (TV) model preserves edges well but causes staircase effects and fails to protect textures. To avoid these limitations, an innovative hybrid regularization model that combines minmax-concave TV (and the shearlet sparsity is proposed for simultaneous image deblurring and image reconstruction. Although the proposed cost function is a non-convex L1-regularized optimization problem, it can maintain the convexity of the cost function by giving the proper nonconvexity parameter to minimize it. Then, an alternating iterative scheme using variable splitting and the alternating direction method of multipliers is introduced to optimize the proposed model. The extensive experiments demonstrate the efficiency and viability of the proposed method in terms of both subjective vision and objective measures.