Graduation Semester and Year
2017
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Ambartsoumian Gaik
Abstract
Image reconstruction in various types of tomography requires inversion of the Radon transform and its generalizations. While there are many stable and robust algorithms for such inversions from reasonably well sampled data, most of these algorithms fail when applied to limited view data. In the dissertation we develop a new method of stable reconstruction from limited view data for functions, whose support is a union of finitely many circles. Such images, among other things, are good approximations of tomograms of certain types of tumors in lungs. Our method is based on a modified version of GPCA (General Principle Component Analysis) and some results from algebraic geometry.
Keywords
GPCA, Radon
Disciplines
Mathematics | Physical Sciences and Mathematics
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Choi, Sl Ghi, "Image Reconstruction from Incomplete Radon Data and Generalized Principal Component Analysis" (2017). Mathematics Dissertations. 177.
https://mavmatrix.uta.edu/math_dissertations/177
Comments
Degree granted by The University of Texas at Arlington