Variational Multiplicative Noise Removal by DC Programming

This paper proposes a difference of convex algorithm (DCA) to deal with a non-convex data fidelity term, proposed by Aubert and Aujol referred to as the AA model. The AA model was adopted in many subsequent works for multiplicative noise removal, most of which focused on convex approximation so that numerical algorithms with guaranteed convergence can be designed. Noting that the AA model can be naturally split into a difference of two convex functions, we apply the DCA to solve the original AA model. Compared to the gradient projection algorithm considered by Aubert and Aujol, the DCA often converges faster and leads to a better solution. We prove that the DCA sequence converges to a stationary point, which satisfies the first order optimality condition. In the experiments, we consider two applications, image denoising and deblurring, both of which involve multiplicative Gamma noise. Numerical results demonstrate that the proposed algorithm outperforms the state-of-the-art methods for multiplicative noise removal.