Mathematics – Probability
Scientific paper
Nov 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000spie.4123..109j&link_type=abstract
Proc. SPIE Vol. 4123, p. 109-114, Image Reconstruction from Incomplete Data, Michael A. Fiddy; Rick P. Millane; Eds.
Mathematics
Probability
Scientific paper
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.
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