Image Restoration through ADMM and Double Sparse Representations

Abstract

Image restoration is a problem because high speed and high restored quality are both very important characteristics a state-of-the-art algorithm should possess. A novel algorithm based on double sparse representations is proposed in this paper to solve the image restoration problem efficiently. A new constrained model whose objective function is the sum of the l2 error term and two different sparse regularized terms is built for the image restoration problem. The alternating direction method of multipliers (ADMM) is applied to optimization problems whose objective functions are the combinations of two convex functions. The method is applicable to the proposed algorithm but with slight adjustments. Through ADMM, the presented restoration model is decomposed into several equivalent sub-problems that are much easier to address. The thresholding functions are employed to solve the non-differentiable z k+1 1 and z k+1 2 sub-problems. The experiments are implemented with several similar algorithms. Compared with other algorithms, the proposed algorithm demonstrates higher speed and obtains better restored quality.