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Directional Wavelet Bases Constructions with Dyadic Quincunx Subsampling

  • Rujie YinEmail author
  • Ingrid Daubechies
Article
  • 183 Downloads

Abstract

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.

Keywords

MRA Directional wavelet bases Perfect reconstruction Dyadic quincunx downsampling Optimization 

Mathematics Subject Classification

42C40 

Notes

Acknowledgements

This work is support by the NSF Grant 1516988.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsDuke UniversityDurhamUSA

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