Non-convexly constrained image reconstruction from nonlinear tomographic X-ray measurements
Non-convexly constrained image reconstruction from nonlinear tomographic X-ray measurements
The use of polychromatic X-ray sources in tomographic X-ray measurements leads to nonlinear X-ray transmission effects. As these nonlinearities are not normally taken into account in tomographic reconstruction, artefacts occur, which can be particularly severe when imaging objects with multiple materials of widely varying X-ray attenuation properties. In these settings, reconstruction algorithms based on a nonlinear X-ray transmission model become valuable. We here study the use of one such model and develop algorithms that impose additional non-convex constraints on the reconstruction. This allows us to reconstruct volumetric data even when limited measurements are available. We propose a nonlinear conjugate gradient iterative hard thresholding algorithm and show how many prior modelling assumptions can be imposed using a range of non-convex constraints.
compressed sensing, inverse problems, nonlinearconstrainedoptimization, tomography
Blumensath, Thomas
470d9055-0373-457e-bf80-4389f8ec4ead
Boardman, Richard P.
5818d677-5732-4e8a-a342-7164dbb10df1
June 2015
Blumensath, Thomas
470d9055-0373-457e-bf80-4389f8ec4ead
Boardman, Richard P.
5818d677-5732-4e8a-a342-7164dbb10df1
Blumensath, Thomas and Boardman, Richard P.
(2015)
Non-convexly constrained image reconstruction from nonlinear tomographic X-ray measurements.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 373 (2043), [20140393].
(doi:10.1098/rsta.2014.0393).
Abstract
The use of polychromatic X-ray sources in tomographic X-ray measurements leads to nonlinear X-ray transmission effects. As these nonlinearities are not normally taken into account in tomographic reconstruction, artefacts occur, which can be particularly severe when imaging objects with multiple materials of widely varying X-ray attenuation properties. In these settings, reconstruction algorithms based on a nonlinear X-ray transmission model become valuable. We here study the use of one such model and develop algorithms that impose additional non-convex constraints on the reconstruction. This allows us to reconstruct volumetric data even when limited measurements are available. We propose a nonlinear conjugate gradient iterative hard thresholding algorithm and show how many prior modelling assumptions can be imposed using a range of non-convex constraints.
Text
Blumensath_JRSA_03_15_r1.pdf
- Author's Original
More information
e-pub ahead of print date: 13 June 2015
Published date: June 2015
Keywords:
compressed sensing, inverse problems, nonlinearconstrainedoptimization, tomography
Organisations:
Signal Processing & Control Grp
Identifiers
Local EPrints ID: 376784
URI: http://eprints.soton.ac.uk/id/eprint/376784
ISSN: 1364-503X
PURE UUID: 9e8fbde2-6641-4691-8d09-6359c57b1033
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Date deposited: 12 May 2015 11:00
Last modified: 15 Mar 2024 03:34
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