Beyond CLEAN

Apart from the difficulties with extended sources, CLEAN as described above is an inherently slow procedure. If $N$ is the number of pixels, subtracting a single source needs of the order of $N$ operations. This seems a waste when this subtraction is a provisional, intermediate step anyway! B.G. Clark had the insight of devising a faster version, which operates with a truncated dirty beam, but only on those maxima in the map strong enough that the far, weak sidelobes make little difference. Once these sources have been identified by this rough CLEAN (called a ``minor cycle''), they are subtracted together from the full map using an fast fourier transform (FFT) for the convolution, which takes only $N \log N$ operations. This is called the ``major cycle''. The new residual map now has a new definition of ``strong'' and the minor cycle is repeated.

A more daring variant, due to Steer, Dewdney, and Ito, (hence SDI CLEAN) carries out the minor cycle by simply identifying high enough maxima, without even using CLEAN, which is kept for the major cycle. Other efforts to cope with extended sources go under the name of ``multiresolution CLEAN''. One could start with the inner part of the $u-v$ plane and do a CLEAN with the appropriate, broader dirty beam. The large scale structure thus subtracted will hopefully now not spoil the next stage of CLEAN at a higher resolution, i.e using more of the $u-v$ plane.