Study On The Recory Of Saprse Under The L₁Norm

Signal acquisition and recovery have put forward for a long time, and have many classic conclusions, the related theory improves gradually. As the development of the times, people put forward high demand of signal sampling rate and the processing speed. While high sampling frequency is time-consuming that can’t meet the demand of the rapid development of the times. Recently, Donoho and others propose a theory called compressive sensing. They put forward that we don’t need a large amount of observations as long as the signal is sparse enough in some transformation. Under certain conditions, the number of observations can be reduced greatly at the same time original signal can be reconstruct with high probability. For the sparse signal reconstruction problem, e1norm minimization provides a convex optimization method which can be turned into a linear programming problem thus substitude e0norm to solve the problem. This paper mainly discusses the feasible ofnorm minimization method in signal recovery and the desired conditions for accuraterecover. As the promotion of thenorm, atomic norm has a strong relationship with compressive sensing. We introduce the idea of atomic norm to provide a good approach for more general problem. Inspired by the e1,norm minimization method, we promote and verify the results in atomic norm. This article consists of the following aspects:(1) Introduce the compressive sensing theory and its mathematical model.(2) Discuss the feasible ofnorm minimization method and the desired conditions for the recovery of sparse vector. (3) Introduce the atomic norm theory and promote the results in e1norm to atomic norm.