Recoverability Analysis for Modified Compressive Sensing with Partially   Known Support
  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. 
Jun Zhang, Yuanqing Li, Zhu Liang Yu and Zhenghui Gu
cs.IT math.IT