A variant of two-step modulus-based matrix splitting iteration method for Retinex problem

Based on a variational optimization model, and by imposing physical constraints on the reflection value, and deriving deformation of the Retinex problem, we find that the Retinex problem is equivalent to a linear complementarity problem and its solution can be computed by solving an equivalent fixed-point equation. In light of the theoretical analysis of the special structure of the system matrix of the linear complementarity problem, we propose a variant of the two-step modulus-based matrix splitting iteration method, and then prove its unconditional convergence. We further give practically quasi-optimal values of the involved iteration parameters in this method. The numerical results show that the variant of the two-step modulus-based matrix splitting iteration method is effective in terms of iteration steps, computing time, and natural image quality evaluator.