Wiener filtering of aliased imagery

We analyze a Fourier-domain Wiener filter for the reconstruction of aliased imagery. The filter is designed to minimize the expected mean square error for the unaliased portion of the object Fourier transform. This analysis yields a net system transfer function, which characterizes the combined effects of the imaging system, sampling, and the reconstruction process, that is valid at both aliased and unaliased spatial frequencies. This transfer function provides insight into how aliasing artifacts are modified by the reconstruction process. Additionally, the net transfer function is useful for characterizing the combined performance of the imaging system and post processing. For example, the net system transfer function can be used to calculate the edge response for reconstructed imagery even in the presence of aliasing. Examples are used to illustrate these aspects of using the Wiener filter with aliased imagery.