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常受到采集噪声的污染。利用图正则化的最新进展，我们提出了一种快速的基于Retinex的复原方案，该方案能够对图像进行去噪和对比度增强。具体而言，根据Retinex理论，我们首先假设每个图像像素是其反射分量和照明分量的乘积。然后，我们假设反射分量和照明分量分别是分段常数（PWC）和连续分段平面（PWP）信号，这些信号可分别通过图拉普拉斯正则化器（GLR）和梯度图拉普拉斯正则化器（GGLR）进行恢复。我们构建了由GLR和GGLR正则化的二次目标函数，通过共轭梯度（CG）法高效求解线性系统（通过所提出的预处理器改善条件数），交替最小化直至收敛。实验结果表明，我们的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。