The theory of tomographical imaging with limited angular input, from which two reconstruction algorithms are derived, is discussed. The existence of missing information because of incomplete angular coverage is demonstrated, and an iteration algorithm to recover this information from <i>a priori</i> knowledge of the finite extent of the object is developed. Smoothing algorithms to stabilize reconstructions in the presence of noise are given. The effects of digitization and finite truncation of the reconstruction region in numerical computation are also analyzed. It is shown that the limited-angle problem is governed by a set of eigenvalues whose spectrum is determined by the imaging angle and the finite extent of the object. The distortion on a point source caused by the missing information is calculated; from the results some properties of the iteration scheme, such as spatial uniformity, are derived.
© 1981 Optical Society of AmericaPDF Article