Graduation Year
2019
Document Type
Thesis
Degree
M.A.
Degree Name
Master of Arts (M.A.)
Degree Granting Department
Mathematics and Statistics
Major Professor
Razvan Teodorescu, Ph.D.
Committee Member
Sherwin Kouchekian, Ph.D.
Committee Member
Wen-Xiu Ma, Ph.D.
Keywords
Integral Transforms, Inverse Problems, QPE, Radon Transform, Attenuation Correction
Abstract
The goal of this study is the recovery of functions and finite parametric distributions from their spherical means over spheres and designing a general formula or algorithm for the reconstruction of a function f via its spherical mean transform. The theoretical study is and supported with a numerical implementation based on radar data. In this study, we approach the reconstruction problem in two different way. The first one is to show how the reconstruction problem could be converted to a Prony-type system of equations. After solving this Prony-type system of equations, one can extract the parameters that describe the corresponding functions or distributions efficiently. The second way is to solve this problem via a backprojection procedure.
Scholar Commons Citation
Pirbudak, Ozan, "Reconstruction of Radar Images by Using Spherical Mean and Regular Radon Transforms" (2019). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/7889
