Abstract

A method of image reconstruction from projections is described which processes the data in polar rather than rectangular coordinates and which does not require back projection. It is based on the decomposition of the object and its shadow (set of projections) into circular harmonics or radial modulators of angular Fourier components. The radial modulators of the object may be reconstructed from those of the shadow using a space-variant system which becomes space-invariant under a coordinate transformation. Experiments using digital and optical implementations are described.

© 1981 Optical Society of America

Theory of circular harmonic image reconstruction

Eric W. Hansen
J. Opt. Soc. Am. 71(3) 304-308 (1981)

Circular and extended circular harmonic transforms and their relevance to image reconstruction from line integrals

Jacques G. Verly
J. Opt. Soc. Am. 71(7) 825-835 (1981)

Tomographic image reconstruction from limited projections using coherent optical feedback

Takuso Sato, Kimio Saski, Yukito Nakamura, Melvin Linzer, and Stephen J. Norton
Appl. Opt. 20(17) 3073-3076 (1981)

Tomographic image reconstruction from limited projections using iterative revisions in image and transform spaces

Takuso Sato, Stephen J. Norton, Melvin Linzer, Osamu Ikeda, and Makoto Hirama
Appl. Opt. 20(3) 395-399 (1981)

Estimation of reconstructions in computed tomography

M. J. Lahart
J. Opt. Soc. Am. 71(10) 1155-1161 (1981)