Sparse sampling recovery by greedy algorithms

TL;DR

This paper analyzes the effectiveness of greedy algorithms, specifically the Weak Chebyshev Greedy Algorithm, for sparse sampling recovery, combining universal discretization and incoherence properties to improve approximation in various norms.

Contribution

It introduces a novel combination of Lebesgue-type inequalities and universal sampling discretization to enhance sparse recovery methods using greedy algorithms.

Findings

WCGA provides good recovery in the Lp norm with proper sampling points.

The approach yields Lebesgue-type inequalities for individual functions.

Error bounds are established for specific classes of multivariate functions.

Abstract

In this paper we analyze approximation and recovery properties with respect to systems satisfying universal sampling discretization property and a special incoherence property. We apply a powerful nonlinear approximation method -- the Weak Chebyshev Greedy Algorithm (WCGA). We establish that the WCGA based on good points for the $L_p$-universal discretization provides good recovery in the $L_p$ norm. For our recovery algorithms we obtain both the Lebesgue-type inequalities for individual functions and the error bounds for special classes of multivariate functions. The main point of the paper is that we combine here two deep and powerful techniques -- Lebesgue-type inequalities for the WCGA and theory of the universal sampling dicretization -- in order to obtain new results in sampling recovery.