Imaging a sectional region within an object with a detector just big e
nough to cover the sectional region-of-interest is analyzed. With othe
rwise complete (for small objects) cone beam scanning configurations,
some of the Radon data are corrupted by unwanted measurements from out
side the region-of-interest, and furthermore the region of corrupted d
ata is in such a shape that the use of a priori information on the fin
ite support of the object alone is not sufficient to recover the missi
ng data. We show that with some suitable choice of scanning configurat
ion and with an innovative method of data combination, all the Radon d
ata can be obtained accurately. The algorithm is mathematically exact,
and requires no iterations and no additional measurements. The method
can be applied to inspect portions of large industrial objects in ind
ustrial imaging, as well as to image portions of human bodies in medic
al diagnosis.