Abstract
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.
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Communicated by Zhong-Zhi Bai.
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Supported by R &D Program of Beijing Municipal Education Commission (No. KM201911232010), P.R. China.
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Chen, F., Zhu, Y. A variant of two-step modulus-based matrix splitting iteration method for Retinex problem. Comp. Appl. Math. 41, 244 (2022). https://doi.org/10.1007/s40314-022-01952-w
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DOI: https://doi.org/10.1007/s40314-022-01952-w
Keywords
- Linear complementarity problem
- Two-step iteration method
- Modulus-based matrix splitting
- Retinex problem