Non-Convex Compressed Sensing Using Partial Support Information

Navid Ghadermarzy; Hassan Mansour; Ozgur Yilmaz

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arXiv · 1311.3773

Non-Convex Compressed Sensing Using Partial Support Information

Navid Ghadermarzy·Hassan Mansour·Ozgur Yilmaz

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Abstract

In this paper we address the recovery conditions of weighted $\ell_p$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that weighted $\ell_p$ minimization with $0<p<1$ is stable and robust under weaker sufficient conditions compared to weighted $\ell_1$ minimization. Moreover, the sufficient recovery conditions of weighted $\ell_p$ are weaker than those of regular $\ell_p$ minimization if at least $50%$ of the support estimate is accurate. We also review some algorithms which exist to solve the non-convex $\ell_p$ problem and illustrate our results with numerical experiments.

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Navid Ghadermarzy, Hassan Mansour, Ozgur Yilmaz. 2013-11-15. Non-Convex Compressed Sensing Using Partial Support Information. https://arxiv.org/abs/1311.3773

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