Fourier spectrum extrapolation and enhancement using support constraints

摘要

The use of support constraints for improving the quality of Fourier spectra estimates is discussed. It is shown that superresolution is an additive phenomenon that is a function of the correlation scale induced by the support constraint, and it is independent of the bandwidth of the measured Fourier spectrum. It is also shown for power spectra that support constraints, due to the enforced correlation of power spectra, reduce the variance of measured power spectra. These theoretical results are validated via computer simulation in the area of speckle interferometry, with very good agreement shown between theory and simulation.