Recovery of Structured Signals With Prior Information via Maximizing Correlation - 2018


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

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