Investigations of the effects of random sampling patterns on the stability of generalized sampling

TL;DR

This paper examines how different random sampling patterns, generated by various spatial point processes, influence the numerical stability of generalized sampling in Fourier and wavelet bases, highlighting the superiority of determinantal processes.

Contribution

It compares the stability effects of binomial, Poisson, and determinantal point processes on non-uniform generalized sampling, emphasizing the advantages of determinantal patterns.

Findings

Determinantal point processes yield more stable sampling patterns.

Regularity in sampling patterns improves numerical stability.

Determinantal processes outperform binomial and Poisson processes in stability.

Abstract

We investigate how the choice of spatial point process for generating random sampling patterns affects the numerical stability of non-uniform generalized sampling between Fourier bases and Daubechies scaling functions. Specifically, we consider binomial, Poisson and determinantal point processes and demonstrate that the more regular point patterns from the determinantal point process are superior.