Robust Spectral Recovery for Dynamical Sampling
2026-04-10 • Information Theory
Information Theory
AI summaryⓘ
The authors study a problem where they try to find the main characteristics (spectrum) of a certain operator from incomplete and noisy data collected over time on a small, circular grid. They point out that current methods have trouble when the data is corrupted at some time points. To fix this, the authors propose a new method that treats the problem as a combination of cleaning incomplete, noisy data using mathematical tools and then applying a spectral estimation technique. Their tests show that this approach recovers the spectrum accurately and is more robust compared to existing methods.
spectral recoverydynamical samplingcircular convolution operatoruniform spatial subsamplingoutlierslow-rank Hankel matrixProny's methodtime-sparse corruptionsrobust estimation
Authors
HanQin Cai, Longxiu Huang, Tianming Wang, Juntao You
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.