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arXiv · 1705.05160

Non-linearity in monochromatic transmission tomography

William R. B. Lionheart·Bjørn Tore Hjertaker·Rachid Maad·Ilker Meric·Sophia B. Coban·Geir Anton Johansen
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Abstract

While it is well known that X-ray tomography using a polychromatic source is non-linear, as the linear attenuation coefficient depends on the wavelength of the X-rays, tomography using near monochromatic sources are usually assumed to be a linear inverse problem. When sources and detectors are not treated as points the measurements are the integrals of the exponentials of line integrals and hence non-linear. In this paper we show that this non-linearity can be observed in realistic situations using both experimental measurements in a gamma-ray tomography system and simulations. We exhibit the Jacobian matrix of the non-linear forward problem. We also demonstrate a reconstruction algorithm, which we apply to experimental data and we show that improved reconstructions can be obtained over the linear approximation.

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William R. B. Lionheart, Bjørn Tore Hjertaker, Rachid Maad, Ilker Meric, Sophia B. Coban, Geir Anton Johansen. 2017-05-15. Non-linearity in monochromatic transmission tomography. https://arxiv.org/abs/1705.05160

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