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Designing Gabor windows using convex optimization

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  • Perraudin, Nathanaël
  • Holighaus, Nicki
  • Søndergaard, Peter L.
  • Balazs, Peter

Abstract

Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal ℓ2-norm dual window, is widely used. This window function however, might lack desirable properties, e.g. good time–frequency concentration, small support or smoothness. We employ convex optimization methods to design dual windows satisfying the Wexler–Raz equations and optimizing various constraints. Numerical experiments suggest that alternate dual windows with considerably improved features can be found.

Suggested Citation

  • Perraudin, Nathanaël & Holighaus, Nicki & Søndergaard, Peter L. & Balazs, Peter, 2018. "Designing Gabor windows using convex optimization," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 266-287.
    • Handle: RePEc:eee:apmaco:v:330:y:2018:i:c:p:266-287
    DOI: 10.1016/j.amc.2018.01.035
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    References listed on IDEAS

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    1. Patrick L. Combettes & Jean-Christophe Pesquet, 2011. "Proximal Splitting Methods in Signal Processing," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 185-212, Springer.
    2. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
    3. Li, Yun-Zhang & Zhang, Yan, 2015. "Vector-valued Gabor frames associated with periodic subsets of the real line," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 102-115.
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    Cited by:

    1. Díaz, Jorge P. & Heineken, Sigrid B. & Morillas, Patricia M., 2023. "Approximate oblique dual frames," Applied Mathematics and Computation, Elsevier, vol. 452(C).

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