In this article, we propose a novel variational model for the joint enhancement and restoration of low-light images corrupted by blurring and/or noise. The model decomposes a given low-light image into reflectance and illumination images that are recovered from blurring and/or noise. In addition, our approach utilizes non-convex total variation regularization on all variables. This allows us to adequately denoise homogeneous regions while preserving the details and edges in both reflectance and illumination images, which leads to clean and sharp final enhanced images. To solve the non-convex model, we employ a proximal alternating minimization approach, and then an iteratively reweighted \(\ell _1\) algorithm and an alternating direction method of multipliers are adopted for solving the subproblems. These techniques contribute to an efficient iterative algorithm, with its convergence proven. Experimental results demonstrate the effectiveness of the proposed model when compared to other state-of-the-art methods in terms of both visual aspect and image quality measures.

在本文中，我们提出了一种新的变分模型，用于联合增强和恢复由于模糊和/或噪声而损坏的低光图像。该模型将给定的低光图像分解为从模糊和/或噪声恢复的反射率图像和照明图像。此外，我们的方法对所有变量都采用非凸的总变化正则化。这使我们能够在对均质区域进行充分去噪的同时保留反射率图像和照明图像中的细节和边缘，从而获得清晰清晰的最终增强图像。为了解决非凸模型，我们采用近端交替最小化方法，然后迭代地加权\（\ ell _1 \）求解子问题，采用算法和乘子的交替方向方法。这些技术有助于有效的迭代算法，并证明了其收敛性。实验结果证明，与其他现有方法相比，该模型在视觉方面和图像质量方面均具有一定的有效性。