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http://dx.doi.org/10.5391/IJFIS.2002.2.1.038

Fast Iterative Solving Method of Fuzzy Relational Equation and its Application to Image Compression/Reconstruction  

Nobuhara, Hajime (Department of Computational Intelligence and System Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technolo)
Takama, Yasufumi (Department of Computational Intelligence and System Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technoloy)
Hirota, Kaoru (Department of Computational Intelligence and System Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technoloy)
Publication Information
International Journal of Fuzzy Logic and Intelligent Systems / v.2, no.1, 2002 , pp. 38-42 More about this Journal
Abstract
A fast iterative solving method of fuzzy relational equation is proposed. It is derived by eliminating a redundant comparison process in the conventional iterative solving method (Pedrycz, 1983). The proposed method is applied to image reconstruction, and confirmed that the computation time is decreased to 1 / 40 with the compression rate of 0.0625. Furthermore, in order to make any initial solution converge on a reconstructed image with a good quality, a new cost function is proposed. Under the condition that the compression rate is 0.0625, it is confirmed that the root mean square error of the proposed method decreases to 27.34% and 86.27% compared with those of the conventional iterative method and a non iterative image reconstruction method, respectively.
Keywords
Fuzzy relational equation; Image compression; Optimization; Gradient method;
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