Jacek Gondzio, Salla-Maaria Latva-Äijö, Samuli M Siltanen, Matti Lassas, Filippo Zanetti,
Abstract
Dual-energy X-ray tomography is considered in a context where the target
under imaging consists of two distinct materials. The materials are assumed to be
possibly intertwined in space, but at any given location there is only one material
present. Further, two X-ray energies are chosen so that there is a clear difference
in the spectral dependence of the attenuation coefficients of the two materials. A
novel regularizer is presented for the inverse problem of reconstructing separate
tomographic images for the two materials. A combination of two things, (a)
non-negativity constraint, and (b) penalty term containing the inner product
between the two material images, promotes the presence of at most one material
in a given pixel. A preconditioned interior point method is derived for the
minimization of the regularization functional. Numerical tests with digital
phantoms suggest that the new algorithm outperforms the baseline method,
Joint Total Variation regularization, in terms of correctly material-characterized
pixels. While the method is tested only in a two-dimensional setting with two
materials and two energies, the approach readily generalizes to three dimensions
and more materials. The number of materials just needs to match the number
of energies used in imaging.
Text
PDF ERGO-21-003.pdf.
History:
Written: June 28, 2021.