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We consider the problem of reconstructing CAT imagery by the direct Fourier method (DFM) when not all view data are available. To restore the missing information we use the method of projections onto convex sets (POCS). POCS is a recursive image restoration technique that finds a solution consistent with the measured data and a priori known constraints in both the space and Fourier domain. Because DFM reconstruction is a frequency-domain technique it is ideally matched to POCS restoration when, for one reason or another, we are forced to generate an image from a less than complete set of view data. We design and apply an algorithm (PRDF) which interpolates/extrapolates the missing Fourier domain information by POCS and reconstructs an image by DFM. A simulated human thorax cross section is restored and reconstructed. The restorations using POCS are compared with the Gerchberg-Papoulis extrapolation method and shown to be superior. Applications of PRDF to other types of medical imaging modalities are discussed.