# Monte Carlo wavelets: a randomized approach to frame discretization

## TL;DR

This paper introduces Monte Carlo wavelets, a stochastic discretization method for continuous wavelets on general domains, leveraging spectral calculus and concentration of measure to ensure convergence and establish rates.

## Contribution

It presents a novel randomized approach to discretize continuous wavelets called Monte Carlo wavelets, with theoretical guarantees of convergence.

## Key findings

- Convergence of Monte Carlo wavelet discretization established
- Derived convergence rates under regularity assumptions
- Applicable to general domains using reproducing kernel Hilbert spaces

## 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.