ERD：基于弱空间和混合非凸正则化的指数Retinex分解及其去噪应用
ERD: Exponential Retinex decomposition based on weak space and hybrid nonconvex regularization and its denoising application
AI总结：
本文提出一种基于混合非凸正则化和弱空间建模的指数Retinex分解去噪模型，利用ADMM和MM算法求解，在PSNR和MSSIM指标上优于现有先进去噪方法。
摘要：
Retinex理论将图像建模为光照分量和反射分量的乘积，该理论受到了广泛关注，并广泛应用于图像增强、图像分割和色彩恢复等领域。然而，由于Retinex含噪图像建模中同时包含乘法和加法运算，该理论很少被用于加性噪声去除。在本文中，我们提出了一种基于混合非凸正则化和弱空间振荡建模的指数Retinex分解模型，用于图像去噪。所提出的模型利用非凸一阶全变分（TV）和非凸二阶TV分别对反射分量和光照分量进行正则化，并采用弱$H^{-1}$范数来度量残差分量。通过使用不同的正则化器，所提出的模型有效地将图像分解为反射分量、光照分量和噪声分量。我们开发了一种结合Majorize-Minimization（MM）算法的交替方向乘子法（ADMM）来求解所提出的模型。此外，我们提供了算法收敛性的详细证明。数值实验验证了所提出的模型和算法的有效性。与几种最先进的去噪模型相比，所提出的模型在峰值信噪比（PSNR）和平均结构相似性（MSSIM）方面表现出更优越的性能。
英文摘要：
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).
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