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.
Kereta, Z., Vigogna, S., Naumova, V., Rosasco, L., De Vito, E. (2019). Monte Carlo wavelets: A randomized approach to frame discretization. In 2019 13th International Conference on Sampling Theory and Applications, SampTA 2019. 345 E 47TH ST, NEW YORK, NY 10017 USA : Institute of Electrical and Electronics Engineers [10.1109/SampTA45681.2019.9030825].
Monte Carlo wavelets: A randomized approach to frame discretization
Vigogna S.;
2019-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
