The quest for optimal sampling: Computationally efficient,   structure-exploiting measurements for compressed sensing
  An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its structure. This paper is about understanding this phenomenon, and demonstrating how it can be fruitfully exploited by the design of suitable sampling strategies in order to outperform more standard compressed sensing techniques based on random matrices. 
Ben Adcock, Anders C. Hansen, Bogdan Roman
math.FA cs.IT math.IT