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Translation Invariant Ri-Spline Wavelet And Its Application On De-Noising

Author

Listed:
  • ZHONG ZHANG

    (Department of Production System Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka Tenpaku-cho, Toyohashi 441-8580, Japan)

  • HIROSHI TODA

    (Faculty of Computer Science and System Engineering, Okayama Prefecture University, 111 Kuboki, 5301 Haga, Soja 719–1197, Japan)

  • HISANAGA FUJIWARA

    (Department of System Engineering, Industrial Technology Center of Okayama, 5301 Haga Okayama-shi, 701-1296, Japan)

  • FUJI REN

    (Faculty of Engineering, The University of Tokushima, 2-1 Minamijosanjima, Tokushima 770-8506, Japan)

Abstract

Wavelet Shrinkage using DWT has been widely used in de-noising although DWT has a translation variance problem. In this study, we solve this problem by using the translation invariant DWT. For this purpose, we propose a new complex wavelet, the Real-Imaginary Spline Wavelet (RI-Spline wavelet). We also propose the Coherent Dual-Tree algorithm for the RI-Spline wavelet and extend it to the 2-Dimensional. Then we apply this translation invariant RI-Spline wavelet for translation invariant de-noising. Experimental results show that our method, when applied to ECG data, the medical image and the textile surface inspection can obtain better de-noising results than that of conventional Wavelet Shrinkage.

Suggested Citation

  • Zhong Zhang & Hiroshi Toda & Hisanaga Fujiwara & Fuji Ren, 2006. "Translation Invariant Ri-Spline Wavelet And Its Application On De-Noising," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 353-378.
    • Handle: RePEc:wsi:ijitdm:v:05:y:2006:i:02:n:s0219622006001976
    DOI: 10.1142/S0219622006001976
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    Cited by:

    1. Yiming Tang & Fuji Ren, 2017. "Fuzzy Systems Based on Universal Triple I Method and Their Response Functions," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 443-471, March.

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