Abel inversion using total-variation regularization
- 10 October 2005
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 21 (6), 1895-1903
- https://doi.org/10.1088/0266-5611/21/6/006
Abstract
In the case of radiography of a cylindrically symmetric object, the Abel transform is useful for describing the tomographic measurement operator. The inverse of this operator is unbounded, so regularization is required for the computation of satisfactory inversions. We introduce the use of the total variation seminorm for this purpose, and prove the existence and uniqueness of solutions of the corresponding variational problem. We illustrate the effectiveness of the total-variation regularization with an example and comparison with the unregularized inverse and the H 1 regularized inverse. (Some figures in this article are in colour only in the electronic version)Keywords
This publication has 8 references indexed in Scilit:
- A numerical method for the discontinuous solutions of Abel integral equationsContemporary Mathematics, 2004
- On the Convergence of the Lagged Diffusivity Fixed Point Method in Total Variation Image RestorationSIAM Journal on Numerical Analysis, 1999
- Iterative Methods for Total Variation DenoisingSIAM Journal on Scientific Computing, 1996
- Nonlinear total variation based noise removal algorithmsPhysica D: Nonlinear Phenomena, 1992
- Darstellung und Kristallstrukturen von Phenyliodoantimonaten(III). Strukturkorrelation für Halogenoantimonate(III) / Preparation and Crystal Structures of Phenyliodoantimonates(III). Structural Correlation for Haloantimonates(III)Zeitschrift für Naturforschung B, 1991
- Abel inversion using transform techniquesJournal of Quantitative Spectroscopy and Radiative Transfer, 1988
- Application of the Abel Integral Equation to Spectrographic DataApplied Optics, 1966
- New Method for Obtaining Emission Coefficients from Emitted Spectral Intensities Part I—Circularly Symmetric Light Sources*Journal of the Optical Society of America, 1965