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Phaseless compressive sensing using partial support information

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Abstract

We study the recovery conditions of weighted \(\ell _1\) minimization for real-valued signal reconstruction from phaseless compressive sensing measurements when partial support information is available. A strong restricted isometry property condition is provided to ensure the stable recovery. Moreover, we present the weighted null space property as the sufficient and necessary condition for the success of k-sparse phaseless recovery via weighted \(\ell _1\) minimization. Numerical experiments are conducted to illustrate our results.

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Acknowledgements

This work is supported by the Swedish Research Council Grant (Reg.No. 340-2013-5342).

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Authors and Affiliations

  1. Department of Statistics, Zhejiang University City College, Hangzhou, 310015, China

    Zhiyong Zhou

  2. Department of Mathematics and Mathematical Statistics, Umeå University, 901 87, Umeå, Sweden

    Jun Yu

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  1. Zhiyong Zhou
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  2. Jun Yu
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Correspondence to Zhiyong Zhou.

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Zhou, Z., Yu, J. Phaseless compressive sensing using partial support information. Optim Lett 14, 1961–1973 (2020). https://doi.org/10.1007/s11590-019-01487-w

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