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Recovery of Structured Signals with Prior Information via Maximizing Correlation. (arXiv:1710.10062v1 [cs.IT])
来源于:arXiv
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. 查看全文>>