Obtaining three-dimensional probability density functions from projected data

Jules S. Jaffe

doi:10.1117/12.409261

16 November 2000 Obtaining three-dimensional probability density functions from projected data

Jules S. Jaffe

Proceedings Volume 4123, Image Reconstruction from Incomplete Data; (2000) https://doi.org/10.1117/12.409261
Event: International Symposium on Optical Science and Technology, 2000, San Diego, CA, United States

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.

Citation Download Citation

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

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