In many experimental observation systems where the goal is to record a 3D observation of an object, or a set of objects, a lower dimensional projection of the intended subject is obtained. In come situations only the statistical properties of such objects is desired: the 3D probability density function. This article demonstrates that under special symmetries this function can be obtained form a 2D probability density function which, has been obtained from the observed, projected data. Standard tomographic theorems can be used to guarantee the uniqueness of this function and a natural basis set can be used in computing the 3D function from the two dimensional projection. Here, the theory of this inversion is explored from a theoretical and numerical point of view with some examples of data functions taken from scientific experiments.

Date Published: 16 November 2000
PDF: 6 pages
Proc. SPIE 4123, Image Reconstruction from Incomplete Data, (16 November 2000);

Published in SPIE Proceedings Vol. 4123:
Image Reconstruction from Incomplete Data
Michael A. Fiddy; Rick P. Millane, Editor(s)