Optimal Sampling Rates in Infinite-Dimensional Compressed Sensing

The theory of compressed sensing studies the problem of recovering a high dimensional sparse vector from its projections onto lower dimensional subspaces. The recently introduced framework of infinite-dimensional compressed sensing [1], to some extent generalizes these results to infinite-dimensional scenarios. In particular, it is shown that the continuous-time signals that have sparse representations in a known domain can be recovered from random samples in a different domain. The range M and the minimum number m of samples for perfect recovery are limited by a balancing property of the two bases. In this paper, by considering Fourier and Haar wavelet bases, we experimentally show that M can be optimally tuned to minimize the number of samples m that guarantee perfect recovery. This study does not have any parallel in the finite-dimensional CS.