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Dual Wavelet Frame Transforms on Manifolds and Graphs

Author

Listed:
  • Lihong Cui
  • Qiaoyun Wu
  • Jiale Liu
  • Jianjun Sun

Abstract

In this paper, we consider the dual wavelet frames in both continuum setting, i.e., on manifolds, and discrete setting, i.e., on graphs. Firstly, we give sufficient conditions for the existence of dual wavelet frames on manifolds by their corresponding masks. Then, we present the formula of the decomposition and reconstruction for the dual wavelet frame transforms on graphs. Finally, we give a numerical example to illustrate the validity of the dual wavelet frame transformation applied to the graph data.

Suggested Citation

  • Lihong Cui & Qiaoyun Wu & Jiale Liu & Jianjun Sun, 2019. "Dual Wavelet Frame Transforms on Manifolds and Graphs," Journal of Mathematics, Hindawi, vol. 2019, pages 1-12, May.
    • Handle: RePEc:hin:jjmath:1637623
    DOI: 10.1155/2019/1637623
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