Sparse approximation of multivariate functions from small datasets via weighted orthogonal matching pursuit

TL;DR

This paper introduces a weighted orthogonal matching pursuit algorithm for efficiently approximating multivariate functions from limited data, achieving accuracy comparable to $ ext{l}^1$ minimization with better computational speed.

Contribution

It extends orthogonal matching pursuit to weighted sparsity, providing a new greedy recovery method for multivariate function approximation from small datasets.

Findings

Achieves accuracy similar to weighted $ ext{l}^1$ minimization.

Significantly improves computational efficiency for small sparsity levels.

Demonstrates effectiveness through numerical experiments.

Abstract

We show the potential of greedy recovery strategies for the sparse approximation of multivariate functions from a small dataset of pointwise evaluations by considering an extension of the orthogonal matching pursuit to the setting of weighted sparsity. The proposed recovery strategy is based on a formal derivation of the greedy index selection rule. Numerical experiments show that the proposed weighted orthogonal matching pursuit algorithm is able to reach accuracy levels similar to those of weighted $\ell^1$ minimization programs while considerably improving the computational efficiency for small values of the sparsity level.