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Discrete Framelet Transforms

Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Discrete wavelet/framelet transforms are the backbone of wavelet theory for its applications in a wide scope of areas. In this chapter we study algorithmic aspects and key properties of wavelets and framelets in the discrete setting. First, we introduce a standard (both one-level and multilevel) discrete framelet transform and filter banks. Then we investigate three fundamental properties of a standard discrete framelet transform: perfect reconstruction, sparsity, and stability; these properties are very much desired and crucial in successful applications of wavelets and framelets.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Bin Han
    • 1
  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada

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