Abstract

We use the method of convex projections to reconstruct a bandlimited function from an arbitrary collection of samples. Each sample is used to define a constraint set of which the unknown function must be a number. For N samples there are N constraint sets and by iteratively alternating between these sets we reconstruct the function. By exploiting the similarity of the projection operators, it is possible to reduce the iterative algorithm to a one-step algorithm. Since we are using the method of convex projections, prior knowledge of the signal can be efficiently used to obtain more rapid convergence. Such prior knowledge might be the energy content of the signal, its similarity or closeness to a reference, and the bounds of its amplitude variations. Our algorithm avoids the need to do the interval averaging¹ used by other authors in attacking the same problem.

© 1989 Optical Society of America