Nonconvex TGV regularization model for multiplicative noise removal with spatially varying parameters

Hanwool Na,Miyoun Jung,Myungjoo Kang,Myeongmin Kang

doi:10.3934/ipi.2019007

Abstract

In this article, we introduce a novel variational model for the restoration of images corrupted by multiplicative Gamma noise. The model incorporates a convex data-fidelity term with a nonconvex version of the total generalized variation (TGV). In addition, we adopt a spatially adaptive regularization parameter (SARP) approach. The nonconvex TGV regularization enables the efficient denoising of smooth regions, without staircasing artifacts that appear on total variation regularization-based models, and edges and details to be conserved. Moreover, the SARP approach further helps preserve fine structures and textures. To deal with the nonconvex regularization, we utilize an iteratively reweighted $\ell_1$ algorithm, and the alternating direction method of multipliers is employed to solve a convex subproblem. This leads to a fast and efficient iterative algorithm for solving the proposed model. Numerical experiments show that the proposed model produces better denoising results than the state-of-the-art models.

Highlights

In many real applications, images unavoidably suffer from noise that occurs during the image-acquisition process
We introduce a nonconvex total generalized variation (TGV) (NTGV)-based model incorporated with the convex data fidelity in [41] to deal with heavy multiplicative noise
The total variation (TV) regularizer was introduced in a variational model for Gaussian noise removal [52]:

Summary

Introduction

Images unavoidably suffer from noise that occurs during the image-acquisition process. Multiplicative Gamma noise, nonconvex total generalized variation, spatially adaptive regularization parameter, iteratively reweighted 1 algorithm, alternating direction method of multiplier. Lu et al [41] suggested a new convex data-fidelity term, which is more suitable for removing heavy multiplicative noise. All these models involve TV regularization, so they tend to produce some artifacts with stair form in smooth transition regions, which are often called staircasing artifacts. Dong et al [18] proposed a new SARP approach for additive Gaussian noise removal with a theoretical analysis This approach was extended to denoising problems with other types of noise [28, 12, 38].

Background

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Conclusions