  We put forward a reconstruction scheme prompted by the relation between a von
Neumann measurement and the corresponding informationally complete measurement
induced in a relevant reconstruction subspace. This method is specially suited
for the full tomography of complex quantum systems, where the intricacies of
the detection part of the experiment can be greatly reduced provided some prior
information is available. In broader terms this shows the importance of
\sugg{this often-disregarded} prior information in quantum theory. The proposed
technique is illustrated with an experimental tomography of photonic vortices
of moderate dimension.
