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.
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