13.7 Deconvolution

The first imaging step presented before leads to a convolution equation whose solution is the convolution product of the sky brightness distribution (apodized by the interferometer primary beam) by the dirty beam.

To derive the astronomically meaningful result, i.e. ideally the sky brightness, a deconvolution is required. Deconvolution is always a non linear process, and requires (in one way or another) to impose some constraints on the solution, or in other words to add some information, to better select plausible solutions. Such additional constraints can be explicit (e.g. positivity, or user specified finite support) or qualitative.