Computer Science – Information Theory
Scientific paper
2012-03-07
Computer Science
Information Theory
11 pages, 5 figures
Scientific paper
Applying the theory of Compressive Sensing in practice always takes different kinds of perturbations into consideration. In this paper, the recovery performance of greedy pursuits with replacement is analyzed when both the measurement vector and the sensing matrix are contaminated with additive perturbations. Specifically, greedy pursuits with replacement include CoSaMP, SP and IHT algorithms, where the support estimation is evaluated and replaced in each iteration. Based on restricted isometry property, a unified form of the error bounds of these recovery algorithms is derived under general perturbations for compressible signals. Derived from the results, the recovery performance is stable against both perturbations. Also, these bounds are compared with that of oracle recovery---least squares solution with the locations of $K$ largest entries in magnitude known a priori. The comparison shows that these bounds only differ in coefficients from the lower bound of oracle recovery with some certain signal and perturbations, as reveals that near-oracle recovery performance of greedy pursuits with replacement is guaranteed. Numerical simulations are performed to verify the conclusions.
Chen Laming
Gu Yuantao
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