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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)
  • Published : 2002.03.01

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.

References

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