A new non-linear superresolution algorithm

A problem receiving considerable attention from researchers is that of producing a stable extrapolation of the Fourier transform of a function of finite support. The problem is ill-posed, and the sensitivity of the extrapolated result to measurement noise is pronounced for many of the solution algorithms proposed to date, In this paper an alternative algorithm is presented. This new algorithm is non-linear, and in certain cases can produce very accurate extrapolations over a wide range of signal-to-noise ratios. We discuss in rather heuristic terms the behavior of this algorithm, and summarize the results of some experiments.