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Parametric Optimization of Biorthogonal Wavelets and Filterbanks via Pseudoframes for Subspaces

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Excursions in Harmonic Analysis, Volume 2

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

Abstract

We present parametric optimizations of biorthogonal wavelets and associated filter banks using pseudoframes for subspaces (PFFS). PFFS extends the theory of frames in that pseudoframe sequences need not reside within the subspace of interest. In particular, when PFFS is applied to biorthogonal wavelets, the underlying flexibility presents opportunities to incorporate optimality, regularity, as well as perfect reconstruction into one parametric design approach. This approach reduces certain filter optimization problems to optimization over a free parameter. While past constructions can be reproduced, results with additional optimality are also obtained and presented here with numerical examples. Tables of filter coefficients along with graphs are provided.

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Acknowledgements

Shidong Li is partially supported by NSF grants DMS-0406979 and DMS-0709384.

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Authors and Affiliations

  1. Department of Mathematics, San Francisco State University, San Francisco, CA, USA

    Shidong Li

  2. Department of Mathematics, Cañada College, Redwood City, CA, USA

    Michael Hoffman

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  1. Shidong Li
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  2. Michael Hoffman
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Correspondence to Shidong Li .

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Editors and Affiliations

  1. , Department of Mathematics, University of Maryland, Norbert Wiener Center, College Park, 20742-0001, Maryland, USA

    Travis D. Andrews

  2. Norbert Wiener Center, Department of Mathematics, University of Maryland, College Park, 20742, Maryland, USA

    Radu Balan

  3. Department of Mathematics, University of Maryland, College Park, 20742-4015, Maryland, USA

    John J. Benedetto

  4. Department of Mathematics, University of Maryland, College Park, 20742-4015, Maryland, USA

    Wojciech Czaja

  5. , Department of Mathematics, University of Maryland, College Park, 20742, Maryland, USA

    Kasso A. Okoudjou

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Li, S., Hoffman, M. (2013). Parametric Optimization of Biorthogonal Wavelets and Filterbanks via Pseudoframes for Subspaces. In: Andrews, T., Balan, R., Benedetto, J., Czaja, W., Okoudjou, K. (eds) Excursions in Harmonic Analysis, Volume 2. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8379-5_7

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