Phaseless compressive sensing using partial support information

We study the recovery conditions of weighted $$\ell _1$$ ℓ 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 $$\ell _1$$ ℓ 1 minimization. Numerical experiments are conducted to illustrate our results.

[1]  Anru Zhang,et al.  Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-Rank Matrices , 2013, IEEE Transactions on Information Theory.

[2]  Zhiqiang Xu,et al.  Phase Retrieval for Sparse Signals , 2013, ArXiv.

[3]  Zhiyong Zhou,et al.  Recovery analysis for weighted mixed l 2 / l p minimization with 0 < p ≤ 1 , 2018 .

[4]  Yuxin Chen,et al.  Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems , 2015, NIPS.

[5]  Naihua Xiu,et al.  Exact Recovery for Sparse Signal via Weighted l_1 Minimization , 2013, ArXiv.

[6]  Xiaodong Li,et al.  Phase Retrieval via Wirtinger Flow: Theory and Algorithms , 2014, IEEE Transactions on Information Theory.

[7]  Rayan Saab,et al.  Weighted ℓ1-Minimization for Sparse Recovery under Arbitrary Prior Information , 2016, ArXiv.

[8]  Prateek Jain,et al.  Phase Retrieval Using Alternating Minimization , 2013, IEEE Transactions on Signal Processing.

[9]  Wengu Chen,et al.  Recovery of signals by a weighted ℓ2/ℓ1 minimization under arbitrary prior support information , 2018, Signal Process..

[10]  Zhiqiang Xu,et al.  A strong restricted isometry property, with an application to phaseless compressed sensing , 2014, ArXiv.

[11]  Holger Rauhut,et al.  A Mathematical Introduction to Compressive Sensing , 2013, Applied and Numerical Harmonic Analysis.

[12]  Hassan Mansour,et al.  Recovering Compressively Sampled Signals Using Partial Support Information , 2010, IEEE Transactions on Information Theory.

[13]  Bing Gao,et al.  Stable Signal Recovery from Phaseless Measurements , 2015, ArXiv.

[14]  Hassan Mansour,et al.  Recovery Analysis for Weighted ℓ1-Minimization Using a Null Space Property , 2014, ArXiv.

[15]  T. Blumensath,et al.  Theory and Applications , 2011 .

[16]  Wengu Chen,et al.  Recovery of signals under the high order RIP condition via prior support information , 2016, Signal Process..

[17]  Yonina C. Eldar,et al.  GESPAR: Efficient Phase Retrieval of Sparse Signals , 2013, IEEE Transactions on Signal Processing.

[18]  Bing Gao,et al.  Phaseless Recovery Using the Gauss–Newton Method , 2016, IEEE Transactions on Signal Processing.

[19]  Yonina C. Eldar,et al.  Phase Retrieval via Matrix Completion , 2011, SIAM Rev..

[20]  Jun Yu,et al.  Recovery analysis for weighted mixed ℓ2∕ℓp minimization with 0p≤1 , 2019, J. Comput. Appl. Math..

[21]  Jun Yu,et al.  Recovery analysis for weighted mixed $\ell_2/\ell_p$ minimization with $0 , 2017, ArXiv.

[22]  S. Sastry,et al.  Compressive Phase Retrieval From Squared Output Measurements Via Semidefinite Programming , 2011, 1111.6323.

[23]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[24]  Emmanuel J. Candès,et al.  PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming , 2011, ArXiv.