Once the dirty beam and the dirty image have been calculated, we want to derive an astronomically meaningful result, ideally the sky brightness. However, it is extremely difficult to recover the intrinsic brightness distribution with an interferometer. But, more fundamentally, the incomplete sampling of the plane implies that there is an infinite number of intensity distributions which are compatible with the constraints given by the measured visibilities. Fortunately, physics allow us to select some solutions from the infinite number that mathematics authorize. The goal of deconvolution is thus to find a sensible intensity distribution compatible with the measured visibilities. To reach this goal, deconvolution needs 1) some a priori, physically valid, assumptions about the source intensity distribution and 2) as much knowledge as possible about the dirty beam and the noise properties (in radioastronomy, both are well known). The best solution would obviously be to avoid deconvolution, i.e. to get a Gaussian dirty beam. For instance, the design of the compact configuration of ALMA has been thought with this goal in mind. However, this goal is out of reach for today millimeter interferometer and it will also be for the extended configuration of ALMA.
The simplest a priori knowledge that the user can feed to deconvolution algorithm is a rough idea of the emitting region in the source. The user defines a support inside which the signal is to be found while the outside is only made of sidelobes. The definition of a support considerably helps the convergence of deconvolution algorithms because it decreases the complexity of the problem (i.e. the size of the space to be searched for solutions). However, it can introduce important biases in the final solution if the support exclude part of the sky region really emitting. Support must be thus used with caution.