Efficient algorithms in irregular sampling of band-limited functions

The author discusses some recent algorithms for the iterative reconstruction of band-limited signals from irregularly sampled values. It is shown that a simplified version of these algorithms allows for a quantitative theory of irregular sampling. The emphasis is on quantitative aspects. Explicit estimates are given for the required sampling density and for the rate of convergence of the iteration algorithm. The author shows that this iteration algorithm converges and yields a complete reconstruction of a band-limited signal from a randomly distributed sampling sequence, provided that the distance between adjacent sampling points is at most the Nyquist distance. An a priori estimate is given on the number of iterations required to achieve a certain accuracy of the approximation to the original signal