Journal article
Abel inversion using total variation regularization: applications
Inverse problems in science and engineering, Vol.14(8), pp.873-885
12/01/2006
Handle:
https://hdl.handle.net/2376/106377
Abstract
We apply total-variation (TV) regularization methods to Abel inversion tomography. Inversions are performed using the fixed-point iteration method and the regularization parameter is chosen such that the resulting data fidelity approximates the known or estimated statistical character of the noisy data. Five one-dimensional (1D) examples illustrate the favorable characteristics of TV-regularized solutions: noise suppression and density discontinuity preservation. Experimental and simulated examples from X-ray radiography also illustrate limitations due to a linear projection approximation. TV-regularized inversions are shown to be superior to squared gradient (Tikhonov) regularized inversions for objects with density discontinuities. We also introduce an adaptive TV method that utilizes a modified discrete gradient operator acting only apart from data-determined density discontinuities. This method provides improved density level preservation relative to the basic TV method.
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Details
- Title
- Abel inversion using total variation regularization: applications
- Creators
- Thomas J Asaki - Continuum Dynamics (CCS-2) , MS D413, Los Alamos National LaboratoryPatrick R Campbell - Mathematical Modeling and Analysis (T-7) , MS B284, Los Alamos National LaboratoryRick Chartrand - Mathematical Modeling and Analysis (T-7) , MS B284, Los Alamos National LaboratoryCollin E Powell - Continuum Dynamics (CCS-2) , MS D413, Los Alamos National LaboratoryKevin R Vixie - Mathematical Modeling and Analysis (T-7) , MS B284, Los Alamos National LaboratoryBrendt E Wohlberg - Mathematical Modeling and Analysis (T-7) , MS B284, Los Alamos National Laboratory
- Publication Details
- Inverse problems in science and engineering, Vol.14(8), pp.873-885
- Academic Unit
- Mathematics and Statistics, Department of
- Publisher
- Taylor & Francis Group
- Identifiers
- 99900546608101842
- Language
- English
- Resource Type
- Journal article