The mathematical generalization of image restoration by recursive methods furnished by D. C. Youla [IEEE Trans. Circuits Syst. <b>CAS 25</b>, 695–702 (1978)] is used to show that arbitrary <i>L</i><sub>2</sub> (i.e., square-integrable) images can be reconstructed from two projections without any <i>a priori</i> 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.
© 1981 Optical Society of AmericaPDF Article