Accuracy of extrapolated spectral values estimated by a function of prior knowledge

The prior discrete Fourier transform (PDFT) is a linear spectral estimator which provides the solution of data consistency and minimum weighted norm through the use of a suitably designed Hilbert space. The PDFT has been successfully used in imaging applications to overcome the nonuniqueness problem due to finitely many measured data. With an appropriate prior function, the resolution of the reconstructed image can be improved dramatically. In particular, for a further understanding we explored a complete and more advanced research about how the available Fourier data and the prior function affect the quality of the PDFT estimate. We address this issue for the purpose of analyzing and evaluating the PDFT in more realistic problems. A relationship between extrapolated spectral values, prior knowledge, and available Fourier data was examined.