Sparse recovery for spherical harmonic expansions

TL;DR

This paper demonstrates that sparse spherical harmonic expansions can be accurately recovered from few random samples on the sphere using compressed sensing techniques, supported by mathematical verification of key properties.

Contribution

It introduces a method to efficiently recover sparse spherical harmonic expansions from limited samples by verifying the restricted isometry property of the measurement matrix.

Findings

Sparse recovery from limited samples is feasible.

Verification of the restricted isometry property for the measurement matrix.

Use of Jacobi polynomial estimates to support the main result.

Abstract

We show that sparse spherical harmonic expansions can be efficiently recovered from a small number of randomly chosen samples on the sphere. To establish the main result, we verify the restricted isometry property of an associated preconditioned random measurement matrix using recent estimates on the uniform growth of Jacobi polynomials.