Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 65, Issue 5, Pages 1506-1525Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S003613990342390X
Keywords
tomographic inversion; probability
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In many experimental observation systems where the goal is to record a three-dimensional observation of an object, or a set of objects, a lower-dimensional projection of the intended subject is obtained. In some situations only the statistical properties of such objects are desired: the three-dimensional probability density function. This article demonstrates that under special symmetries this function can be obtained from either a one- or two-dimensional 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 three-dimensional function from the one- or two-dimensional projection. The theory of this inversion is explored using theoretical and computational methods with examples of data taken from scientific experiments.
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