Superresolution capabilities of the Gerchberg method in the band‐pass case: An eigenvalue analysis

This article first provides a general introduction to the Gerchberg superresolution algorithm. Some specific properties of this algorithm, when applied to 2D band-pass images, are then studied by means of an eigenvalue analysis of the imaging operator. The main feature derived is the capability to recover the dc component of the unknown object that has to be reconstructed from the noisy image available. This aspect is important with band-pass images of strictly positive objects, in that recovering the low-frequency and dc components in this case is tantamount to suppressing intolerable artifacts. A set of eigenpairs of the imaging operator was calculated numerically. From the dominant eigenvalues, the spectrum extrapolation capabilities of the method can be derived. From the behavior of the eigenfunctions, the capability of the method to recover the dc component of the original object can be evaluated. Some of the calculated eigenfunctions are shown as examples