Since its introduction by Högbom (1974), ‘clean’ has been widely used to restore images from the aperture synthesis techniques of radio astronomy. The method iteratively subtracts from the maximum deflection of the image the point source response and so deconvolves it with some loop gain;

where yn = residue image.

xn = deconvolving beam derived by matching the peak of the beam to where yn has the maximum deflection and band-limiting the size of beam within the image,

An = a scalar in accordance with the loop gain applied to the residue image, and

n = iteration.

Ideally, the residue image converges to noise level. In digital processing, the method is implemented with special purpose hardware, general purpose computer, or array processor. In all cases the image to be restored (the ‘dirty’ map), the space-invariant beam used to deconvolve the image (the ‘dirty’ antenna pattern) and the loop gain are stored in binary format in memories and registers with finite wordlength. (Wordlength is an economic factor both in hardware and software implementations).