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Publication Detail
Monte Carlo wavelets: A randomized approach to frame discretization
  • Publication Type:
    Journal article
  • Publication Sub Type:
    Article
  • Authors:
    Kereta Z, Vigogna S, Naumova V, Rosasco L, De Vito E
  • Publication date:
    12/03/2020
  • Journal:
    2019 13th International Conference on Sampling Theory and Applications, SampTA 2019
  • Status:
    Published
Abstract
© 2019 IEEE. In this paper we propose and study a family of continuous wavelets on general domains, and a corresponding stochastic discretization that we call Monte Carlo wavelets. First, using tools from the theory of reproducing kernel Hilbert spaces and associated integral operators, we define a family of continuous wavelets by spectral calculus. Then, we propose a stochastic discretization based on Monte Carlo estimates of integral operators. Using concentration of measure results, we establish the convergence of such a discretization and derive convergence rates under natural regularity assumptions.
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