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.