An effective dual method for multiplicative noise removal

•This is the first paper that studies the problem with total variation constrain for multiplicative noise removal.•We prove and give the dual formula of the primal problem.•We give an efficient dual algorithm for our proposed model.•We give a fast algorithm based on split and duality to accelerate the rate of convergence for our proposed model.

The problem of multiplicative noise removal has been widely studied recently, but most models focus on the unconstrained problems. These models require knowing the prior level of noise beforehand, however, the information is not obtained in some case and the regularization parameters are not easy to be adjusted. Thus, in the paper, we mainly study an optimization problem with total variation constraint, and propose two new denoising algorithms which compute the projection on the set of images whose total variation is bounded by a constant. In the first algorithm, we firstly give the dual formula of our model, then compute the dual problem using alternating direction method of multipliers. Experimental results show that our method is simple and efficient to filter out the multiplicative noise when the prior of noise is unknown.