Robust Spectral Recovery for Dynamical Sampling

2026-04-10

AI Summary

This work addresses the challenge of spectral recovery for an unknown circulant convolution operator under dynamic sampling, where temporally sparse outliers severely degrade reconstruction accuracy. The authors propose a robust spectral recovery method that, for the first time, integrates robust low-rank Hankel matrix recovery with Prony-type spectral estimation. By reformulating the original problem as a sequence of robust Hankel matrix recovery and completion tasks, the approach effectively mitigates the adverse effects of outlier contamination and substantially enhances spectral estimation accuracy. Numerical experiments demonstrate that the method reliably recovers spectra across diverse scenarios and exhibits markedly superior robustness compared to state-of-the-art techniques.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Non-convex Optimization
• Machine Learning: Matrix & Tensor Methods

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

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.

Problem

• spectral recovery
• dynamical sampling
• outliers
• time-sparse corruptions
• circular convolution

Innovation

• robust spectral recovery
• dynamical sampling
• low-rank Hankel recovery
• time-sparse corruptions
• Prony-type estimation