Superresolution through error function extrapolation

Using the constrained iterative algorithm, it is shown that superresolution can be achieved by extrapolating the error function in the image as well as by extrapolating the spectrum of a band-limited function. It is shown, on the basis of a single cycle of the constrained iterative algorithm, that the eigenvectors corresponding to an eigenvalue of 1 are easy to obtain and that these are the vectors out of which a perfect recreation could be made. A figure of merit for noise, the noise amplification, is given, and several problems are evaluated with it. It is also shown that noise amplification in the recreation could be traded for bandwidth by band limiting the eigenvectors corresponding to the eigenvalue of 1. When the signal-to-noise ratio of the data is available, a reasonable basis for placing error bars on the enhanced images is described