Pushing the RIP phase transition in compressed sensing

We apply the asymmetric restricted isometry property (ARIP) to recent results of Cai, Wang, and Xu and formulate a two-parameter family of sufficient conditions for exact k-sparse signal recovery via ℓ
¹
-minimization. We translate the sufficient conditions into the phase transition framework and apply bounds on the ARIP constants to define lower bounds on the phase transition. By selecting the parameters wisely, we determine sufficient conditions whose phase transition curves improve upon those already in the literature.