Abstract

Distinguishing signal from noise has always been a major goal in probabilistic analysis of data. Such is no less the case in the field of medical imaging, where both the processes of photon emission and their rate of absorption by the body behave as random variables. We explore methods by which to extricate solid conclusions from noisy data involving an X-ray transform, long the mathematical mainstay of such tools as computed axial tomography (CAT scans). Working on the assumption of having some prior probabilities assigned to various states a body can be found in, we introduce and make rigorous an understanding of how to condition these into posterior probabilities by using the scan data.

Notes

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Graduation Date

2017

Semester

Summer

Advisor

Swanson, Jason

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematics

Format

application/pdf

Identifier

CFE0006740

URL

http://purl.fcla.edu/fcla/etd/CFE0006740

Language

English

Release Date

8-15-2022

Length of Campus-only Access

5 years

Access Status

Doctoral Dissertation (Open Access)

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Included in

Mathematics Commons

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