SUPERRESOLUTION CAPABILITIES OF THE GERCHBERG METHOD IN THE BAND-PASSCASE - AN EIGENVALUE ANALYSIS

This article first provides a general introduction to the Gerchberg su perresolution algorithm. Some specific properties of this algorithm, w hen applied to 2D band-pass images, are then studied by means of an ei genvalue analysis of the imaging operator. The main feature derived is the capability to recover the do component of the unknown object that has to be reconstructed from the noisy image available. This aspect i s important with band-pass images of strictly positive objects, in tha t recovering the low-frequency and do components in this case is tanta mount to suppressing intolerable artifacts. A set of eigenpairs of the imaging operator was calculated numerically. From the dominant eigenv alues, the spectrum extrapolation capabilities of the method can be de rived. From the behavior of the eigenfunctions, the capability of the method to recover the dc component of the original object can be evalu ated. Some of the calculated eigenfunctions are shown as examples. (C) 1998 John Wiley & Sons, Inc.