On Approximation of Bandlimited Functions with Compressed Sensing

The application of Compressed Sensing techniques to bandlimited functions is investigated in this paper. It is shown that under the assumption of sparsity, stable reconstruction of a bandlimited function is possible from finitely many samples, contrary to classical results from signal processing theory. The number of measurements that need to be taken is proportional to the sparsity of the function. In compact intervals, it is shown that the number of pointwise measurements required scales quadratically with the size of the largest expansion coefficient (in a basis in which sparsity is measured) which is sufficient for a faithful function approximation.