Multiplicative Noise Removal Based on the Linear Alternating Direction Method for a Hybrid Variational Model

Abstract

To preserve the edge, multiplicative noise removal models based on the total variation regularization have been widely studied, but they suffer from the staircase effect. In this paper, to preserve the edge and reduce the staircase effect, we develop a hybrid variational model based on the variable splitting method for multiplicative noise removal; the new model is a strictly convex objective function which contains the total variation regularization and a modified regularization term. We use the linear alternative direction method to find the minimal solution and also give the convergence proof of the proposed algorithm. Experimental results verify that the proposed model can obtain the better results for removing the multiplicative noise compared with the recent method.

Euler’s elastica and curvature based model for image restoration

“…Yu Hao et. al proposed a new hybrid variational model and method (in 2017) [ 59 ] based on variable splitting for multiplicative removal as follows; where ξ = log ( f ) and v is a vector field of the image ξ . Also λ > 0, α > 0, and β > 0 are the regularizer parameters.…”

“…In this subsection, we have compared the two models, i.e., method M3 and proposed method M2 for image restoration for the same images with the same size and noise variance along with same parameters values as selected in [ 59 ]. We can see that the results obtained by our proposed method M2 are outstanding in the visual quality of restoration (PSNR), eliminating the staircase effect and preserving the textures.…”