Volume 12, Issue 2
A Modulus Iteration Method for SPSD Linear Complementarity Problem Arising in Image Retinex

Adv. Appl. Math. Mech., 12 (2020), pp. 579-598.

Published online: 2020-01

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• Abstract

Retinex theory explains that the image intensity is the product of the object's reflectance and illumination. However, the true color of the object in the image is determined only by the reflectance of the object. The purpose of retinex problem is to decompose the reflectance from the image intensity. In this paper, a new variational model with physical constraint imposed on the reflectance is proposed. The proposed model can be transformed to a linear complementarity problem (LCP) with symmetric positive semi-definite (SPSD) matrix. The main contribution of the paper is that the LCP with SPSD matrix is solved by the modulus iteration method and the convergence is demonstrated. Experiments numerically show the effectiveness of the proposed method for retinex problem and the convergence of the modulus iteration method for solving the LCP with SPSD matrix.

• AMS Subject Headings

65Y99, 68U10

yangxue2014@lzu.edu.cn (Xue Yang)

huangym@lzu.edu.cn (Yu-Mei Huang)

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@Article{AAMM-12-579, author = {Yang , Xue and Huang , Yu-Mei}, title = {A Modulus Iteration Method for SPSD Linear Complementarity Problem Arising in Image Retinex}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {2}, pages = {579--598}, abstract = {

Retinex theory explains that the image intensity is the product of the object's reflectance and illumination. However, the true color of the object in the image is determined only by the reflectance of the object. The purpose of retinex problem is to decompose the reflectance from the image intensity. In this paper, a new variational model with physical constraint imposed on the reflectance is proposed. The proposed model can be transformed to a linear complementarity problem (LCP) with symmetric positive semi-definite (SPSD) matrix. The main contribution of the paper is that the LCP with SPSD matrix is solved by the modulus iteration method and the convergence is demonstrated. Experiments numerically show the effectiveness of the proposed method for retinex problem and the convergence of the modulus iteration method for solving the LCP with SPSD matrix.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0207}, url = {http://global-sci.org/intro/article_detail/aamm/13635.html} }
TY - JOUR T1 - A Modulus Iteration Method for SPSD Linear Complementarity Problem Arising in Image Retinex AU - Yang , Xue AU - Huang , Yu-Mei JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 579 EP - 598 PY - 2020 DA - 2020/01 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0207 UR - https://global-sci.org/intro/article_detail/aamm/13635.html KW - Linear complementarity problem, modulus iteration method, image retinex, symmetric positive semi-definite. AB -

Retinex theory explains that the image intensity is the product of the object's reflectance and illumination. However, the true color of the object in the image is determined only by the reflectance of the object. The purpose of retinex problem is to decompose the reflectance from the image intensity. In this paper, a new variational model with physical constraint imposed on the reflectance is proposed. The proposed model can be transformed to a linear complementarity problem (LCP) with symmetric positive semi-definite (SPSD) matrix. The main contribution of the paper is that the LCP with SPSD matrix is solved by the modulus iteration method and the convergence is demonstrated. Experiments numerically show the effectiveness of the proposed method for retinex problem and the convergence of the modulus iteration method for solving the LCP with SPSD matrix.

Xue Yang & Yu-Mei Huang. (2020). A Modulus Iteration Method for SPSD Linear Complementarity Problem Arising in Image Retinex. Advances in Applied Mathematics and Mechanics. 12 (2). 579-598. doi:10.4208/aamm.OA-2019-0207
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