16 November 2000 Obtaining three-dimensional probability density functions from projected data
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Abstract
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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Jules S. Jaffe, Jules S. Jaffe, } "Obtaining three-dimensional probability density functions from projected data", Proc. SPIE 4123, Image Reconstruction from Incomplete Data, (16 November 2000); doi: 10.1117/12.409261; https://doi.org/10.1117/12.409261
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