Directional Wavelet Bases Constructions with Dyadic Quincunx Subsampling

Journal Article (Journal Article)

We construct directional wavelet systems that will enable building efficient signal representation schemes with good direction selectivity. In particular, we focus on wavelet bases with dyadic quincunx subsampling. In our previous work (Yin, in: Proceedings of the 2015 international conference on sampling theory and applications (SampTA), 2015), we show that the supports of orthonormal wavelets in our framework are discontinuous in the frequency domain, yet this irregularity constraint can be avoided in frames, even with redundancy factor <2. In this paper, we focus on the extension of orthonormal wavelets to biorthogonal wavelets and show that the same obstruction of regularity as in orthonormal schemes exists in biorthogonal schemes. In addition, we provide a numerical algorithm for biorthogonal wavelets construction where the dual wavelets can be optimized, though at the cost of deteriorating the primal wavelets due to the intrinsic irregularity of biorthogonal schemes.

Full Text

Duke Authors

Cited Authors

  • Yin, R; Daubechies, I

Published Date

  • June 1, 2018

Published In

Volume / Issue

  • 24 / 3

Start / End Page

  • 872 - 907

International Standard Serial Number (ISSN)

  • 1069-5869

Digital Object Identifier (DOI)

  • 10.1007/s00041-017-9540-z

Citation Source

  • Scopus