Robust Spectral Recovery for Dynamical Sampling
This addresses a robustness issue in dynamical sampling for signal processing applications, though it appears incremental as it builds on existing spectral recovery frameworks.
The paper tackles the problem of recovering the spectrum of a circular convolution operator from time snapshots with sparse corruptions, proposing a robust pipeline that achieves accurate spectral recovery and demonstrates superior robustness compared to state-of-the-art methods.
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.