Images captured in poorly lit conditions are often corrupted by acquisition noise. Leveraging recent advances in graph-based regularization, we propose a fast Retinex-based restoration scheme that denoises and contrast-enhances an image. Specifically, by Retinex theory we first assume that each image pixel is a multiplication of its reflectance and illumination components. We next assume that the reflectance and illumination components are piecewise constant (PWC) and continuous piecewise planar (PWP) signals, which can be recovered via graph Laplacian regularizer (GLR) and gradient graph Laplacian regularizer (GGLR) respectively. We formulate quadratic objectives regularized by GLR and GGLR, which are minimized alternately until convergence by solving linear systems -- with improved condition numbers via proposed preconditioners -- via conjugate gradient (CG) efficiently. Experimental results show that our algorithm achieves competitive visual image quality while reducing computation complexity noticeably.

翻译：在弱光条件下拍摄的图像常伴有采集噪声。借鉴基于图的正则化最新进展，我们提出一种快速Retinex复原方案，可同时实现图像去噪与对比度增强。具体而言，基于Retinex理论，我们首先假设每个图像像素是反射分量与光照分量的乘积，继而假设反射分量与光照分量分别为分段常数（PWC）信号和连续分段平面（PWP）信号，并分别通过图拉普拉斯正则化（GLR）和梯度图拉普拉斯正则化（GGLR）进行恢复。我们构建了以GLR和GGLR正则化的二次目标函数，通过共轭梯度法（CG）交替求解线性系统直至收敛——其中利用所提出的预处理器改善条件数。实验结果表明，本算法在显著降低计算复杂度的同时，实现了具有竞争力的视觉图像质量。