We consider the problem of reconstructing an object function f(r) from finitely many linear functional values. In our main application, the function f(r) is a tomographic image, and the data are integrals of f(r) along thin strips. Because the data are limited, resolution can be enhanced through the inclusion of prior knowledge. One way to do that, a generalization of the prior discrete Fourier transform (PDFT) method, was suggested in 1982 [SIAM J. Appl. Math.42,933 (1982)] but was found to be difficult to implement for the tomography problem, and that application was not pursued. Recent advances in approximating the PDFT make it possible to achieve the desired resolution enhancement in an easily implemented procedure.