Recovery of Structured Signals with Prior Information via Maximizing Correlation

TL;DR

This paper introduces a correlation-maximization method for recovering structured signals from noisy measurements using prior knowledge, providing theoretical guarantees and demonstrating improved performance over standard methods.

Contribution

A novel approach that incorporates prior information into signal recovery by maximizing correlation, with theoretical analysis and practical validation.

Findings

Performance guarantees under sub-Gaussian measurements

Effective for sparse, block-sparse, and low-rank signals

Outperforms standard recovery when prior info is accurate

Abstract

This paper considers the problem of recovering a structured signal from a relatively small number of noisy measurements with the aid of a similar signal which is known beforehand. We propose a new approach to integrate prior information into the standard recovery procedure by maximizing the correlation between the prior knowledge and the desired signal. We then establish performance guarantees (in terms of the number of measurements) for the proposed method under sub-Gaussian measurements. Specific structured signals including sparse vectors, block-sparse vectors, and low-rank matrices are also analyzed. Furthermore, we present an interesting geometrical interpretation for the proposed procedure. Our results demonstrate that if prior information is good enough, then the proposed approach can (remarkably) outperform the standard recovery procedure. Simulations are provided to verify our results.