Adaptive Compressed Sensing for Support Recovery of Structured Sparse Sets

TL;DR

This paper explores adaptive compressive sensing techniques for support recovery of structured sparse signals, demonstrating near-optimal protocols that outperform non-adaptive methods by leveraging structure and adaptivity.

Contribution

It introduces adaptive sensing protocols tailored for structured support sets, achieving significant performance improvements over traditional non-adaptive approaches.

Findings

Adaptive sensing improves support recovery accuracy.

Structured support sets enable more efficient sensing strategies.

Adaptive protocols outperform non-adaptive methods in noisy environments.

Abstract

This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering such sets through compressive measurements, while simultaneously providing adaptive support recovery protocols that perform near optimally for these classes. We show that by adaptively designing the sensing matrix we can attain significant performance gains over non-adaptive protocols. These gains arise from the fact that adaptive sensing can: (i) better mitigate the effects of noise, and (ii) better capitalize on the structure of the support sets.