Direct Reconstruction Of Three Dimensional Image From Its Line Integrals

Atsushi Imiya; Hidemitsu Ogawa

doi:10.1117/12.966676

1 January 1986 Direct Reconstruction Of Three Dimensional Image From Its Line Integrals

Atsushi Imiya, Hidemitsu Ogawa

Proceedings Volume 0671, Physics and Engineering of Computerized Multidimensional Imaging and Processing; (1986) https://doi.org/10.1117/12.966676
Event: Physics and Engineering of Computerized Multidimensional Imaging and Processing, 1986, Newport Beach, CA, United States

Abstract

This paper proposes a series expansion method for the direct reconstruction of a three dimensional image from its line integrals. We clarify a relation between line integrals and plane integrals of a three dimensional image. The relation yields a pair of basis functions in the image space and the projection space. The basis functions are similar to the singular functions of the Radon transformation. Since projection data are practically obtainable along a finite number of beams, we also propose a reconstruction formula which is expressed by a finite sum of products of sampled radiographs and a set of functions. The present reconstruction method is applicable to any incomplete projections and any scanning modes.

Citation Download Citation

Atsushi Imiya and Hidemitsu Ogawa "Direct Reconstruction Of Three Dimensional Image From Its Line Integrals", Proc. SPIE 0671, Physics and Engineering of Computerized Multidimensional Imaging and Processing, (1 January 1986); https://doi.org/10.1117/12.966676

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