Three-Dimensional Probability Density Functions via Tomographic Inversion

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-dimens...

Full description

Saved in:
Bibliographic Details
Published inSIAM journal on applied mathematics Vol. 65; no. 5; pp. 1506 - 1525
Main Author Jaffe, Jules S.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2005
Subjects
Animals
Cameras
Data collection
Data ranges
Datasets
Density distributions
Fourier transforms
Geometric planes
Geometric shapes
Histograms
Mathematical functions
Sonar
Symmetry
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0036-1399
1095-712X
DOI:10.1137/S003613990342390X