The Cotton-Schwab algorithm

 

Cotton & Schwab (Schwab 1984b, top right corner of p. 1078!) developed a variant of the Clark algorithm whereby the major cycle subtracts `CLEAN' components from the un-gridded visibility data. Aliasing noise and gridding errors can thus be removed if the inverse Fourier transform of the `CLEAN' components to each u,v sample is accurate enough. Two routes are used for the inverse transform:

1. for small numbers of `CLEAN' components, a `direct Fourier transform' is performed so the accuracy is limited by the precision of the arithmetic;
2. for a large number of `CLEAN' components, an FFT is used for efficiency, but inevitably some errors are introduced in interpolating from the grid to each u,v sample. High order Lagrangian interpolation is generally used.

A further advantage of the Cotton-Schwab algorithm, besides gridding correction, is its ability to image and `CLEAN' many separate but proximate fields simultaneously. In the minor cycle each field is `CLEAN'ed independently; in the major cycles, `CLEAN' components from all fields are removed together. In calculating the residual image for each field, the full phase equation, including the w-term, can be used. Thus, the algorithm can correct images for the ``non-coplanar baselines'' distortion.

The Cotton-Schwab algorithm is often faster than the Clark `CLEAN', the major exception being for data sets with a large number of visibility samples, where re-gridding many times can be prohibitively expensive. The Cotton-Schwab algorithm also allows `CLEAN'ing with smaller guard bands around the region of interest, hence with smaller image sizes.

The algorithm has been particularly useful for `CLEAN'ing sensitive, high-resolution images at lower radio frequencies where there may be numerous confusing sources in the primary beam. In such work, imaging a wide field of view to deconvolve the sidelobes of distant confusing sources in a Högbom or Clark `CLEAN' could be prohibitively expensive in disk space and time. The confusing sources (once identified from a diagnostic low-resolution image) can however be handled in small sub-fields using the Cotton-Schwab approach.

The Cotton-Schwab algorithm was first implemented in the NRAO's Astronomical Image Processing System (classic AIPS) as the program `MX' and is now the basis of the AIPS programs `IMAGR' and `WFCLN'.

1996 November 4
10:52:31 EST