ERD: Exponential Retinex decomposition based on weak space and hybrid nonconvex regularization and its denoising application

TL;DR

This paper introduces an exponential Retinex decomposition model with hybrid non-convex regularization and weak space modeling, specifically designed for image denoising, demonstrating superior performance over existing methods.

Contribution

It proposes a novel Retinex-based denoising model using hybrid non-convex regularization and weak space norms, along with an efficient ADMM-Majorize-Minimization algorithm with proven convergence.

Findings

Outperforms state-of-the-art denoising models in PSNR and MSSIM

Effectively decomposes images into reflection, illumination, and noise components

Provides a convergent algorithm with theoretical guarantees

Abstract

The Retinex theory models the image as a product of illumination and reflection components, which has received extensive attention and is widely used in image enhancement, segmentation and color restoration. However, it has been rarely used in additive noise removal due to the inclusion of both multiplication and addition operations in the Retinex noisy image modeling. In this paper, we propose an exponential Retinex decomposition model based on hybrid non-convex regularization and weak space oscillation-modeling for image denoising. The proposed model utilizes non-convex first-order total variation (TV) and non-convex second-order TV to regularize the reflection component and the illumination component, respectively, and employs weak $H^{-1}$ norm to measure the residual component. By utilizing different regularizers, the proposed model effectively decomposes the image into reflection, illumination, and noise components. An alternating direction multipliers method (ADMM) combined with the Majorize-Minimization (MM) algorithm is developed to solve the proposed model. Furthermore, we provide a detailed proof of the convergence property of the algorithm. Numerical experiments validate both the proposed model and algorithm. Compared with several state-of-the-art denoising models, the proposed model exhibits superior performance in terms of peak signal-to-noise ratio (PSNR) and mean structural similarity (MSSIM).