On Stability of Sampling-Reconstruction Models

TL;DR

This paper investigates the stability of sampling-reconstruction models under various small perturbations, providing theoretical guarantees and using localized frames to analyze recovery robustness.

Contribution

It proves stability results for a broad class of sampling models and introduces a framework to quantify their robustness against different perturbations.

Findings

Sampling models are stable under small perturbations.

The robustness of models is quantified for various perturbation classes.

Localized frames effectively analyze signal recovery stability.

Abstract

A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this paper we prove this result for a large class of sampling models. We define different classes of perturbations and quantify the robustness of a model with respect to them. We also use the theory of localized frames to study the frame algorithm for recovering the original signal from its samples.