Efficient multiplicative noise removal method using isotropic second order total variation

To overcome and reduce the undesirable staircase effect commonly met in the total variation (TV) regularization based multiplicative noise removal methods, a novel multiplicative noise removal model based on isotropic second order total variation (ISOTV) is proposed under the maximum a posteriori (MAP) framework. Under the spectral decomposition framework, the ISOTV is first transformed into an equivalent formulation as a novel weighted L1–L2L1–L2 mixed norm of the second order image derivatives. Then an efficient alternating iterative algorithm is designed to solve the proposed model. Finally, we prove in detail the convergence of the proposed algorithm. A set of experiments on both standard and medical images show that the proposed ISOTV method yields state-of-the-art results both in terms of peak signal to noise ratio (PSNR) and image perception quality. Specifically, the proposed ISOTV method can better reduce the staircase effect and preserve image edges more sharpness with medical applications.