Infinite-dimensional compressed sensing and function interpolation (Q1656376)

In this paper the author gives a framework and series of recovery guarantees for the use of compressed sensing (CS) in approximating multivariate functions from limited numbers of point-wise samples. In this framework the recovery problem is formulated as a minimization problem in an infinite-dimensional space and then is discretized. This work provides a theoretical basis for a number of recent numerical studies showing the effectiveness of much approaches.