A generic tool for analyzing sparse approximation algorithms is the restricted isometry property (RIP) introduced by Candès and Tao. For qualitative comparison of sufficient conditions derived from an RIP analysis, the support size of the RIP constants is generally reduced as much as possible with the goal of achieving a support size of twice the sparsity of target signal. Using a quantitative comparison via phase transitions for Gaussian meaurement matrices, three examples from the literature of such support size reduction are investigated. In each case, utilizing a larger support size for the RIP constants results in a weaker sufficient condition for exact sparse recovery.
Compressed sensing, restricted isometry constants, restricted isometry property, signal recovery, sparse approximation
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