Monte Carlo wavelets: a randomized approach to frame discretization
Functional Analysis
2021-03-09 v2 Machine Learning
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.
Cite
@article{arxiv.1903.06594,
title = {Monte Carlo wavelets: a randomized approach to frame discretization},
author = {Zeljko Kereta and Stefano Vigogna and Valeriya Naumova and Lorenzo Rosasco and Ernesto De Vito},
journal= {arXiv preprint arXiv:1903.06594},
year = {2021}
}