A Derivative Augmented Lagrangian Method for Fast Total Variation Based Image Restoration

Abstract

In this paper, we propose a novel derivative augmented Lagrangian method for fast total variation (TV) based image restoration (TVIR). By introducing a novel variable splitting method, TVIR is approximately reformulated in the derivative space, resulting in a constrained convex optimization problem which is simple to solve. Then, we propose a derivative alternating direction method of multipliers (D-ADMM) to solve the derivative space image restoration problem. Furthermore, we provide a Fourier domain updating algorithm which can save two fast Fourier transform (FFT) operations per iteration. Experimental results show that, compared with the state-of-the-art algorithms, D-ADMM is more efficient and can achieve satisfactory restoration quality.