The use of support constraints for improving the quality of Fourier spectra and their associated images is discussed as well as the relationship between the two domains. Theoretical relationships are derived that predict the noise reduction in both the image domain and the Fourier domain achieved by single and repeated application of support constraints for the case of wide-sense stationary Fourier-domain noise. It is shown that the application of support constraints can increase noise inside the support constraint if the application is not done correctly. An iterative algorithm is proposed that enforces support constraints in such a way that noise is never increased inside the support constraint and the algorithm achieves the minimum possible noise in a finite number of steps.
© 1994 Optical Society of America
Original Manuscript: March 10, 1993
Manuscript Accepted: June 23, 1993
Published: January 1, 1994
Charles L. Matson, "Variance reduction in Fourier spectra and their corresponding images with the use of support constraints," J. Opt. Soc. Am. A 11, 97-106 (1994)