The AIPS task APCLN performs what is known as a Clark CLEAN (Clark 1980). This is a variant on the original Högbom algorithm, which spends a lot of time shifting and scaling the dirty beam. This is essentially a convolution, and may in some circumstances be more efficiently performed with an FFT. For very small images though, the Högbom CLEAN may still be faster.
The Clark CLEAN plays a few tricks which you should know about. It has what are termed major and minor cycles. In the minor cycle, clean components are searched for, and subtracted from the image, in a fashion very similar to that of the Högbom CLEAN. The difference is that only the central portion of the dirty beam is used for the subtraction. The rationale is that for dirty beams that have a fairly good sidelobe pattern, this will be good enough to find the CLEAN components. At some designated time, this minor cycle is terminated and a major cycle computed. This means that the list of CLEAN components from the current cycle are 'FFTd', and subtracted from the FFT of the residual image that resulted from the previous major cycle. In this way, errors that might have accumulated in the subtraction phase of the minor cycle with only a part of the beam are largely set to rights. Because of the FFT, a Högbom CLEAN can be more efficient than a Clark CLEAN on small images.
This use of a small beam patch in the Clark CLEAN is a potential danger if the beam is poor. Images made from ATCA snapshot data, even if there are a few cuts, often have a beam in which the first side lobe response is quite strong and outside of the beam patch that the Clark CLEAN typically uses. I will discuss this more in the discussion below of the AIPS\ tasks that do a Clark CLEAN.