Interferometic CLEAN Algorithm

The CLEAN algorithm (Hogbom 1974) is essentially a brute force deconvolution. The starting point is the fact that the measured dirty image Id 0x. y) is the convolution of the true intensity or sky map I(6x, 9y) with the dirty beam B(0x, 9y), this is 

Although working in the Fourier domain seems like an option to recover the sky map by dividing the Fourier transfer of IniB, By) by the Fourier transform of B(Bx, By) which is the Mv-map, in practice the Fourier transform of B(6x, By) contains areas where it is zero and thus this is not an option (Thompson et al. 1986). The problem arises from the fact that the v-map is sparse. 

Interpolating the v-map can also arbitrarily generate information which is not present in the initial sky map. Basically, one wants the visibility at non-sampled v-map positions to take values consistent with the most reasonable or likely intensity distribution while minimising the addition of arbitrary detail. 

The CLEAN algorithm is vastly used and is one of the most successM iterative deconvolution algorithms which attempts to obtain an image compatible with the data assuming it is made of point-like sources. 

CLEAN is aimed for point sources or compact sources. However, once the point sources from a dirty beam have been removed, the residual dirty image is essentially due to the extended sources which may be smooth enough to not be too distorted by the convolution with the dirty beam. For this reason, the residual dirty image can be added to the clean image to create the final image. 

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