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A construction method for data adapted wavelet

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Abstract

A construction method is proposed for a biorthogonal wavelet which approximates an arbitrarily given target function. This method is expected to be useful in the cases where the given data is a superposition of the target functions dilated and translated. The biorthogonal wavelet then provides an efficient decomposition of the given data into the elements of events. The biorthogonal wavelet is obtained by Lagrange’s multiplier method minimizing the L2-norm of the difference between the target function and the primary wavelet. As an example, this method is applied to the Mexican hat function as a target function, to produce a biorthogonal wavelet close to the Mexican hat.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguroku, 153-8914, Tokyo, Japan

    Michio Yamada

  2. I. T. Solutions Department, Kajima Corporation, 5-30 Akasaka 6-chome, Minatoku, 107-8502, Tokyo, Japan

    Fumio Sasaki

Authors
  1. Michio Yamada
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  2. Fumio Sasaki
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Correspondence to Michio Yamada.

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Yamada, M., Sasaki, F. A construction method for data adapted wavelet. Japan J. Indust. Appl. Math. 18, 307–320 (2001). https://doi.org/10.1007/BF03168577

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  • DOI: https://doi.org/10.1007/BF03168577

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