2012/07/08 by Jun Zhang, Zhang, Jun, Yuanqing Li +5
Computer Science · Engineering · Mathematics · #Blind Source Separation Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Microwave Imaging and Scattering Analysis #Sparse and Compressive Sensing Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1207.1855
arxiv created 2012/07/08 · openalex publication_date 2012/07/08 · arxiv updated 2012/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℓ nonzero entries, even though the known support exists some errors. Simulation experiments have been carried out to validate our theoretical results.