Effect of errors in partially known support on the recoverability of modified compressive sensing

Abstract

The recently proposed modified compressive sensing (modified-CS), which utilizes the partially known support as prior knowledge, significantly improves the performance of compressive sensing. In practice, the known part will inevitably involve some errors, which may degrade the gain of modified-CS. Within the stochastic framework, this article discuss the effect of errors in known part on the recoverability of modified-CS. First, based on the probabilistic measure of recoverability, two probability inequalities on recoverability are established, which reflect the changing tendencies of the recoverability of modified-CS with respect to the addition of errors in the known support and sparsity of original sparse vector. A direct corollary reveals further the effect degree of recoverability as adding an error in known support. Second, the maximum number of errors that the modified-CS can bear is also analyzed. We prove a quantitative-bound of errors in known part that relates with the number of samples and the sparsity of original vector. This bound mirrors the fault-tolerance capability of modified-CS. Simulation experiments have been carried out to validate our theoretical results. © 2012 Zhang et al.