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
![](//static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20180308043702250-0594:S0252921100074935:S0252921100074935_inline01.gif?pub-status=live)
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.