Restoration of arbitrary finite-energy optical objects from limited spatial and spectral information

The mathematical generalization of image restoration by recursive methods furnished by D. C. Youla [ IEEE Trans. Circuits Syst.CAS 25, 695– 702 ( 1978)] is used to show that arbitrary L2 (i.e., square-integrable) images can be reconstructed from two projections without any a priori assumption regarding the mathematical properties of the object, such as space-limitedness or band-limitedness. Recursive algorithms are given to restore images from (1) extended segments and low-pass spectra and (2) short segments and high-pass spectra. Using the alternating projection theorem, we prove monotonic convergence (in the norm) to the original image.