PERFECT-TRANSLATION-INVARIANT CUSTOMIZABLE COMPLEX DISCRETE WAVELET TRANSFORM

DOI Web Site 1 Citations
  • HIROSHI TODA
    Department of Production System Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka Tenpaku-cho, Toyohashi 441-8580, Japan
  • ZHONG ZHANG
    Department of Production System Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka Tenpaku-cho, Toyohashi 441-8580, Japan
  • TAKASHI IMAMURA
    Department of Production System Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka Tenpaku-cho, Toyohashi 441-8580, Japan

Bibliographic Information

Published
2013-07
DOI
  • 10.1142/s0219691313600035
Publisher
World Scientific Pub Co Pte Lt

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<jats:p> The theorems, giving the condition of perfect translation invariance for discrete wavelet transforms, have already been proven. Based on these theorems, the dual-tree complex discrete wavelet transform, the 2-dimensional discrete wavelet transform, the complex wavelet packet transform, the variable-density complex discrete wavelet transform and the real-valued discrete wavelet transform, having perfect translation invariance, were proposed. However, their customizability of wavelets in the frequency domain is limited. In this paper, also based on these theorems, a new type of complex discrete wavelet transform is proposed, which achieves perfect translation invariance with high degree of customizability of wavelets in the frequency domain. </jats:p>

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