Regression in large p, small n setting has attracted much recent attention in sev eral fields including statistics, applied mathematics and engineering.In this talk I will discuss recovery of high dimensional sparse signals in three settings: noiseless, bounded error and Gaussian noise.I will present an elementary and unified treat mcnt in these noise settings for two l1 minimization methods: the Dantzig selector and l1 minimization with an l2 constraint.Our results improve the existing ones in the literature by weakening the conditions and tightening the error bounds.The im provement on the conditions shows that signals with larger support can be recovered accurately.