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arXiv · 1207.1855

Recoverability Analysis for Modified Compressive Sensing with Partially Known Support

Jun Zhang·Yuanqing Li·Zhu Liang Yu·Zhenghui Gu
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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 \ell nonzero entries, even though the known support exists some errors. Simulation experiments have been carried out to validate our theoretical results.

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Jun Zhang, Yuanqing Li, Zhu Liang Yu, Zhenghui Gu. 2012-07-08. Recoverability Analysis for Modified Compressive Sensing with Partially Known Support. https://arxiv.org/abs/1207.1855

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