  We study here sparse recovery problems in the presence of additive noise. We
analyze a thresholding version of the CoSaMP algorithm, named Thresholding
Greedy Pursuit (TGP). We demonstrate that an appropriate choice of thresholding
parameter, even without the knowledge of sparsity level of the signal and
strength of the noise, can result in exact recovery with no false discoveries
as the dimension of the data increases to infinity.
