Retinex theory was proposed by Land in the 1970s. Its theoretical basis is that the color of an object is determined by the reflection ability of the object to the light of long wave, medium wave, and short wave, rather than by the absolute value of the reflected light intensity. There is color sense consistency in Retinex theory. The main purpose of Retinex problem is to recover the reflection properties of objects from the images obtained under a certain illumination intensity, so as to obtain the real colors of objects. There are many methods for solving the Retinex problem. In this paper, based on a variational minimization model with physical constraints of reflectance value, we first transform the Retinex problem into a linear complementarity problem, and then propose a class of two-step modulus-based matrix splitting iteration methods to solve this problem. We also prove the convergence of the two-step modulus-based matrix splitting iteration methods for solving the linear complementarity problem. The experimental results show that the convergence speeds of the proposed methods are much faster than the existing methods for solving the Retinex problem, and that the advantages of the new methods over the existing ones could be significant in the quality of the reflectance recovery.

Retinex理论是Land在1970年代提出的。其理论基础是，对象的颜色取决于对象对长波，中波和短波的反射能力，而不是反射光强度的绝对值。Retinex理论中存在色觉一致性。Retinex问题的主要目的是从在一定照明强度下获得的图像中恢复物体的反射特性，从而获得物体的真实色彩。有很多方法可以解决Retinex问题。在本文中，基于具有反射率值物理约束的变分最小化模型，我们首先将Retinex问题转化为线性互补问题，然后提出了一种基于两步模量的矩阵分裂迭代方法来解决这一问题。我们还证明了求解线性互补问题的基于两步模量的矩阵分裂迭代方法的收敛性。实验结果表明，所提出的方法的收敛速度比现有的解决Retinex问题的方法要快得多，并且与现有方法相比，新方法的优势可能在反射率恢复质量上具有重要意义。