Fast Iterative Solving Method of Various Types of Fuzzy Relational Equations and its Application to Image Reconstruction
Hajime Nobuhara, Yasufumi Takama and Kaoru Hirota
Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku Yokohama 226-8502 Japan
A fast iterative solving method of various types of fuzzy relational equations is proposed. This method 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 1/39 – 1/45 with the compression rate of 0.0625. Furthermore, in order to make any initial solution converge on a reconstructed image with 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 24.00% and 86.03% compared with those of the conventional iterative method and a non iterative image reconstruction method (Nobuhara, 2001), respectively.
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