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.

翻译：我们在这里研究在添加性噪音面前的稀有回收问题。我们分析了CoSaMP算法的临界值版本,名为TGP(TGP ) 。 我们证明,即使不知道信号的宽度和噪音的强度,如果选择适当的临界值参数(即使不知道信号的宽度和噪音的强度)可以导致精确的回收,而随着数据范围逐渐扩大,没有虚假的发现。