Non-convexly constrained image reconstruction from nonlinear tomographic X-ray measurements

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) (doi:10.1098/rsta.2014.0393).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1098/rsta.2014.0393
ISSNs: 1364-503X (print)
Keywords: compressed sensing, inverse problems, nonlinearconstrainedoptimization, tomography
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Organisations: Signal Processing & Control Grp
ePrint ID: 376784
Date :
Date Event
4 May 2015e-pub ahead of print
June 2015Published
Date Deposited: 12 May 2015 11:00
Last Modified: 17 Apr 2017 06:16
Further Information:Google Scholar

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