A new difference of anisotropic and isotropic total variation regularization method for image restoration

Total variation (TV) regularizer has diffusely emerged in image processing. In this paper, we propose a new nonconvex total variation regularization method based on the generalized Fischer-Burmeister function for image restoration. Since our model is nonconvex and nonsmooth, the specific difference of convex algorithms (DCA) are presented, in which the subproblem can be minimized by the alternating direction method of multipliers (ADMM). The algorithms have a low computational complexity in each iteration. Experiment results including image denoising and magnetic resonance imaging demonstrate that the proposed models produce more preferable results compared with state-of-the-art methods

Group sparse representation and saturation-value total variation based color image denoising under multiplicative noise

In this article, we propose a novel group-based sparse representation (GSR) model for restoring color images in the presence of multiplicative noise. This model consists of a convex data-fidelity term, and two regularizations including GSR and saturation-value-based total variation (SVTV). The data-fidelity term is suitable for handling heavy multiplicative noise. GSR enables the retention of textures and details while sufficiently removing noise in smooth regions without producing the staircase artifacts engendered by total variation-based models. Furthermore, we introduce a multi-color channel-based GSR that involves coupling between three color channels. This avoids the generation of color artifacts caused by decoupled color channel-based methods. SVTV further improves the visual quality of restored images by diminishing certain artifacts induced by patch-based methods. To solve the proposed nonconvex model and its subproblem, we exploit the alternating direction method of multipliers, which contributes to an efficient iterative algorithm. Numerical results demonstrate the outstanding performance of the proposed model compared to other existing models regarding visual aspect and image quality evaluation values

Variational models for multiplicative noise removal

학위논문 (박사)-- 서울대학교 대학원 자연과학대학 수리과학부, 2017. 8. 강명주.This dissertation discusses a variational partial differential equation (PDE) models for restoration of images corrupted by multiplicative Gamma noise. The two proposed models are suitable for heavy multiplicative noise which is often seen in applications. First, we propose a total variation (TV) based model with local constraints. The local constraint involves multiple local windows which is related a spatially adaptive regularization parameter (SARP). In addition, convergence analysis such as the existence and uniqueness of a solution is also provided. Second model is an extension of the first one using nonconvex version of the total generalized variation (TGV). The nonconvex TGV regularization enables to efficiently denoise smooth regions, without staircasing artifacts that appear on total variation regularization based models, and to conserve edges and details.1. Introduction 1 2. Previous works 6 2.1 Variational models for image denoising 6 2.2.1 Convex and nonconvex regularizers 6 2.2.2 Variational models for multiplicative noise removal 8 2.2 Proximal linearized alternating direction method of multipliers 10 3. Proposed models 13 3.1 Proposed model 1 :exp TV model with SARP 13 3.1.1 Derivation of our model 13 3.1.2 Proposed TV model with local constraints 16 3.1.3 A SARP algorithm for solving model (3.1.16) 27 3.1.4 Numerical results 32 3.2 Proposed model 2 :exp NTGV model with SARP 51 3.2.1 Proposed NTGV model 51 3.2.2 Updating rule for $\lambda(x)$ in (3.2.1) 52 3.2.3 Algorithm for solving the proposed model (3.2.1) 55 3.2.4 Numerical results 62 3.2.5 Selection of parameters 63 3.2.6 Image denoising 65 4. Conclusion 79Docto