An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the object to recover, but also on its structure. This chapter 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.
Adcock, B., Hansen, A. C., & Roman, B. (2015). The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing. In Applied and Numerical Harmonic Analysis (pp. 143–167). Springer International Publishing. https://doi.org/10.1007/978-3-319-16042-9_5