Wiener filtering and cleaning in a general image processing context

• Published in: Monthly notices of the Royal Astronomical Society Vol. 211; no. 1; pp. 1 - 14
• Main Authors: Bates, J. H. T., Fright, W. R., Bates, R. H. T.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Oxford University Press 01.11.1984; Blackwell Science
• Subjects: Astronomy; Earth, ocean, space; Exact sciences and technology; Fundamental astronomy and astrophysics. Instrumentation, techniques, and astronomical observations; Observation and data reduction techniques. Computer modeling and simulation; Image processing; Algorithm
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/211.1.1

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. While this algorithm can often be usefully invoked when the image is ‘extended’, the convergence is slower and less certain, which has led to modifications of CLEAN. It is shown here that Cornwell's recent modification 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 straight-forwardly. It is suggested that Wiener filtering might be advantageously invoked after the number of cleaning iterations has been sufficient to raise the amplitudes of the majority of the initially missing Fourier samples well above the noise level.