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.
| Identifer | oai:union.ndltd.org:USF/oai:scholarcommons.usf.edu:etd-9086 |
| Date | 28 June 2019 |
| Creators | Pirbudak, Ozan |
| Publisher | Scholar Commons |
| Source Sets | University of South Flordia |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Graduate Theses and Dissertations |
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