Accelerated Chambolle Projection Algorithms for Image Restoration

Abstract

In this paper, the accelerated Chambolle projection algorithms based on Frank–Wolfe have been proposed. For solving the image restoration under the additive Gaussian noise, the Chambolle projection method (CP) is widely used. However, the projection operator has a large computational cost and complex form. By means of the Frank–Wolfe method, this projection operation can be greatly simplified. We propose two new algorithms, called Chambolle projection based on Frank–Wolfe (CP–FW) and Chambolle projection based on accelerated Frank–Wolfe (CP–AFW). They have a fast convergence rate and low computation cost. Furthermore, we extend the new algorithms to deal with the Poisson noise. The convergence of the new algorithms is discussed, and results of the experiment show their effectiveness and efficiency.