Compression using Quasi-Interpolation

TL;DR

This paper explores quasi-interpolation techniques for radial basis function approximation and data compression, providing convergence, error estimates, and insights into nonlinear approximation and low-smoothness functions.

Contribution

It introduces new convergence and error estimates for quasi-interpolants, advancing understanding of wavelet-based compression and approximation methods.

Findings

Error estimates for nonlinear approximation by quasi-interpolation

Results on compression in continuous function spaces

Pointwise convergence for low-smoothness functions

Abstract

We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from their linear spaces and provide convergence estimates. The results include an error estimate for nonlinear approximation by quasi-interpolation, results about compression in the space of continuous functions and a pointwise convergence estimate for approximands of low smoothness.