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.

Automated summary

Based on a variational optimization model and physical constraints, this study establishes the equivalence between the Retinex problem and a linear complementarity problem. By solving an equivalent fixed-point equation, the solution of the Retinex problem can be computed. A variant of the two-step modulus-based matrix splitting iteration method is proposed and its unconditional convergence is proven. Numerical results demonstrate the effectiveness of this method in terms of iteration steps, computing time, and natural image quality evaluator.