Robust Spectral Recovery for Dynamical Sampling

TL;DR

This paper introduces a robust spectral recovery method for dynamical sampling on finite cyclic grids, effectively handling outliers and improving accuracy over existing techniques.

Contribution

A novel robust spectral recovery model using low-rank Hankel recovery and Prony-type estimation, enhancing robustness against corruptions in dynamical sampling.

Findings

Accurately recovers spectra in the presence of outliers.

Outperforms existing methods in robustness and accuracy.

Validated through numerical experiments.

Abstract

We study the spectral recovery problem for dynamical sampling on a finite cyclic grid. Given time snapshots obtained from a fixed uniform spatial subsampling of the orbit $x_{\ell}=A^{\ell}f$, we aim to recover the spectrum of the unknown circular convolution operator $A$. However, in the presence of outliers, even in only a few snapshots, existing approaches often struggle to recover the spectrum. We address this challenge by proposing a novel robust spectral recovery model in the presence of time-sparse corruptions. We propose a robust pipeline that lifts the problem to a sequence of robust low-rank Hankel recovery and completion tasks, followed by Prony-type spectral estimation. Numerical experiments confirm the accurate spectral recovery of the proposed approach and exhibit its superior robustness against state-of-the-art under various settings.