Recoverability Analysis for Modified Compressive Sensing with Partially Known Support
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.
Cite
@article{arxiv.1207.1855,
title = {Recoverability Analysis for Modified Compressive Sensing with Partially Known Support},
author = {Jun Zhang and Yuanqing Li and Zhu Liang Yu and Zhenghui Gu},
journal= {arXiv preprint arXiv:1207.1855},
year = {2012}
}