Smoothed projection methods for the moment problem

Summary We discuss the problem of reconstructing a functionf from a finite set of moments. Problems of this kind typically arise as discretizations of integral equations of the first kind. We propose an algorithm which is based on a pointwise optimization of the pointspread function, which makes it particularly suitable for local reconstructions. The method is compared with known methods as Backus-Gilbert and projection methods. Convergence of the method is proved and the rate of convergence is determined. The influence of noisy data is examined and numerical examples show the usefulness of the method.