||Depth Resolution in 3D Imaging
||Larsen, Elin Aalders
||Hansen, Per Christian (Scientific Computing, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
||Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
||In this thesis we develop software for experimenting with, and analyzing potential-field inversion. The software includes two module-based GUIs, one for magnetic-field inversion in 2D and one for potential-field inversion in 3D. The GUIs make
it possible for users to use state-of-the-art techniques to perform experiments
with inverse potential-field problems without the need to understand or implement
the underlying mathematics. The modules of the GUIs are created
such that people with a mathematical and numerical background can use the
functionalities of the GUIs separate from the GUIs.
Relevant theory about inverse problems and discretization of inverse problems
is presented. The regularization methods Truncated SVD, Tikhonov and CGLS
are discussed in standard and in general form. Furthermore smoothing norms
in the form of derivative smoothing and depth weighting are derived.
Experiments with potential-field inversions are conducted in order to establish
the reconstruction capabilities and the depth resolution of potential-field problems.
We also perform tests of whether incorporating a priori information in the
form of either derivative smoothing or depth weighting can improve the depth
resolution of a problem.
This thesis also includes the manuals for the two implemented GUIs.
||Technical University of Denmark (DTU) : Kgs. Lyngby, Denmark
Creation date: 2010-06-23
Update date: 2010-08-16