Recovery of Structured Signals with Prior Information via Maximizing Correlation

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.

27 pages, 27 figures

References in corpus (2)

• Compressed Sensing with Prior Information: Optimal Strategies, Geometry, and Bounds
• Compressed Sensing with Prior Information via Maximizing Correlation

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• Spectrally Sparse Signal Recovery via Hankel Matrix Completion with Prior Information
• Multi-dimensional Spectral Super-Resolution with Prior Knowledge via Frequency-Selective Vandermonde Decomposition and ADMM
• Matrix Completion with Prior Subspace Information via Maximizing Correlation