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arXiv · 1903.06594

Monte Carlo wavelets: a randomized approach to frame discretization

Zeljko Kereta·Stefano Vigogna·Valeriya Naumova·Lorenzo Rosasco·Ernesto De Vito
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Abstract

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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Zeljko Kereta, Stefano Vigogna, Valeriya Naumova, Lorenzo Rosasco, Ernesto De Vito. 2019-03-15. Monte Carlo wavelets: a randomized approach to frame discretization. https://arxiv.org/abs/1903.06594

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