On recovery of sparse signals via l1 minimization

This article considers constrained l1 minimization methods for the recovery of high dimensional sparse signals in three settings: noiseless, bounded error and Gaussian noise. A unified and elementary treatment is given in these noise settings for two l1 minimization methods: the Dantzig selector and l1 minimization with an l2 constraint. The results of this paper improve the existing results in the literature by weakening the conditions and tightening the error bounds. The improvement on the conditions shows that signals with larger support can be recovered accurately. This paper also establishes connections between restricted isometry property and the mutual incoherence property. Some results of Candes, Romberg and Tao (2006) and Donoho, Elad, and Temlyakov (2006) are extended.