A common problem in radio synthesis work is that of determining the brightness at N grid points in the map domain when there are only n<N independent interferometer measurements available. The missing (N-n) equations can in principle be replaced by an equivalent amount of information in the form of a priori knowledge about the brightness distribution. One way of doing this is to add an equation of the form

i.e. some function of the brightness distribution is maximized subject to the condition that the map be compatible with the n measurements. This automatically gives (N-n) new equations, leaving us in the pleasant situation of having as many equations as there are unknowns.