Wiener filtering and cleaning in a general image processing context

The algorithm CLEAN is known to be effective for removing sidelobes from an image of Fourier transformed incomplete data when the true image consists of isolated point sources. It is shown here that Cornwell's recent modification of CLEAN is closely related to another result (established in this paper): by cleaning with a dirty beam that has been modified in accord with the Wiener approach to deconvolution, clean maps are obtained equivalent to those produced by the conventional two stage procedure of cleaning followed by reconvolving with a clean beam. It is argued both that the standard theory of the Wiener filter is inappropriate in most image processing contexts and that the filter's operation should be interpreted more straightforwardly.