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Performance estimation of sparse signal recovery under Bernoulli random projection with oracle information

This article discusses the performance of the oracle receiver in recovering high dimensional sparse signals, which possesses the knowledge of the signals' support set. We consider a general framework, in which the sensing matrix and the measurements are disturbed simultaneously. The entries of the sensing matrix are i.i.d. Bernoulli random variables. We introduce the lower and upper bounds of the normalized mean square error of the reconstruction, which are proved to hold with high probability and verified by numerical simulations. The result is then compared with previous works on Gaussian sensing matrices. The average recovery error is derived as a generalization of the conclusion in [12] for the Gaussian ensemble and measurement noise only case.