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Signal recovery under mutual incoherence property and oracle inequalities

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Abstract

We consider the signal recovery through an unconstrained minimization in the framework of mutual incoherence property. A sufficient condition is provided to guarantee the stable recovery in the noisy case. Furthermore, oracle inequalities of both sparse signals and non-sparse signals are derived under the mutual incoherence condition in the case of Gaussian noises. Finally, we investigate the relationship between mutual incoherence property and robust null space property and find that robust null space property can be deduced from the mutual incoherence property.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11871109), NSAF (Grant No. U1830107), and the Science Challenge Project (TZ2018001).

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Authors and Affiliations

  1. Graduate School, China Academy of Engineering Physics, Beijing, 100088, China

    Peng Li

  2. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Wengu Chen

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  1. Peng Li
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  2. Wengu Chen
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Correspondence to Wengu Chen.

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Li, P., Chen, W. Signal recovery under mutual incoherence property and oracle inequalities. Front. Math. China 13, 1369–1396 (2018). https://doi.org/10.1007/s11464-018-0733-9

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  • DOI: https://doi.org/10.1007/s11464-018-0733-9

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