The exciting new field of compressed sensing concerns efficient recovery of sparse signals from considerably fewer (linear) measurements. This technique of information processing has numerous potential applications in areas including statistics, medical imaging, decoding and encryption.

In this talk, we shall describe a family of RIP conditions that ensure the reconstruction of sparse data via convex minimization, for compressed sensing matrices. Some simple conditions which are of theoretical and practical interest can be deduced from this family. The main ingredients of our approach include the norm inequality and the square-root lifting inequality. The improvement on the conditions shows that signals with larger support can be recovered accurately. Issues on compressed sensing matrix design and our complete solution of sparse recovery in the mutual incoherence framework will also be touched on.

 

(Joint work with Tony Cai and Lie Wang.)