Accuracy of extrapolated data as a function of prior knowledge and regularization

The prior discrete Fourier transform (PDFT) is a linear spectral estimator that provides a solution that is both data consistent and of minimum weighted norm through the use of a suitably designed Hilbert space. The PDFT has been successfully used in imaging applications to improve resolution and overcome the nonuniqueness associated with having only finitely many spectral measurements. With the use of an appropriate prior function, the resolution of the reconstructed image can be improved dramatically. We explore the ways in which some significant parameters affect the PDFT estimate. A relationship between estimated spectral values, prior knowledge, and regularization was examined. It allows one to assess the reliability of the estimated spectral values for a given choice of prior estimate and provides a means for optimizing PDFT-based estimators.