A New Convex Optimization Model for Multiplicative Noise and Blur Removal

Abstract

The main contribution of this paper is to propose a new convex optimization model for multiplicative noise and blur removal. The main idea is to rewrite a blur and multiplicative noise equation such that both the image variable and the noise variable are decoupled. The resulting objective function involves the total variation regularization term, the term of variance of the inverse of noise, the $\ell_1$-norm of the data-fitting term among the observed image, and noise and image variables. Such a convex minimization model can be solved efficiently by using many numerical methods in the literature. Numerical examples are presented to demonstrate the effectiveness of the proposed model. Experimental results show that the proposed model can handle blur and multiplicative noise (Gamma, Gaussian, or Rayleigh distribution) removal quite well.