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).

翻译：Retinex理论将图像建模为光照分量与反射分量的乘积，已获得广泛关注并广泛应用于图像增强、分割与色彩恢复。然而，由于Retinex噪声图像建模同时包含乘法和加法运算，该理论在加性噪声去除中鲜有应用。本文提出一种基于混合非凸正则化与弱空间振荡建模的指数Retinex分解模型用于图像去噪。该模型分别采用非凸一阶全变差（TV）与非凸二阶TV正则化反射分量与光照分量，并利用弱$H^{-1}$范数度量残差分量。通过使用不同的正则化器，该模型能有效将图像分解为反射、光照与噪声分量。本文开发了结合Majorize-Minimization（MM）算法的交替方向乘子法（ADMM）来求解所提模型。此外，我们详细证明了算法的收敛性质。数值实验验证了所提模型与算法的有效性。与多种先进去噪模型相比，所提模型在峰值信噪比（PSNR）和平均结构相似性（MSSIM）指标上均表现出更优性能。