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Recoverability Analysis for Modified Compressive Sensing with Partially Known Support

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  • Jun Zhang
  • Yuanqing Li
  • Zhenghui Gu
  • Zhu Liang Yu

Abstract

The recently proposed modified-compressive sensing (modified-CS), which utilizes the partially known support as prior knowledge, significantly improves the performance of recovering sparse signals. However, modified-CS depends heavily on the reliability of the known support. An important problem, which must be studied further, is the recoverability of modified-CS when the known support contains a number of errors. In this letter, we analyze the recoverability of modified-CS in a stochastic framework. A sufficient and necessary condition is established for exact recovery of a sparse signal. Utilizing this condition, the recovery probability that reflects the recoverability of modified-CS can be computed explicitly for a sparse signal with nonzero entries. Simulation experiments have been carried out to validate our theoretical results.

Suggested Citation

  • Jun Zhang & Yuanqing Li & Zhenghui Gu & Zhu Liang Yu, 2014. "Recoverability Analysis for Modified Compressive Sensing with Partially Known Support," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-7, February.
    • Handle: RePEc:plo:pone00:0087985
    DOI: 10.1371/journal.pone.0087985
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