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Non-Convex Compressed Sensing Using Partial Support Information

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Abstract

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

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, BC, Canada

    Navid Ghadermarzy & Özgür Yılmaz

  2. Mitsubishi Electric Research Laboratories, Cambridge, MA, 02139, USA

    Hassan Mansour

Authors
  1. Navid Ghadermarzy
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  2. Hassan Mansour
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  3. Özgür Yılmaz
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Additional information

This work was conducted while Hassan Mansour was a postdoctoral research fellow in the Mathematics Department at the University of British Columbia.

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Ghadermarzy, N., Mansour, H. & Yılmaz, Ö. Non-Convex Compressed Sensing Using Partial Support Information. STSIP 13, 249–270 (2014). https://doi.org/10.1007/BF03549582

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