Non-linearity in monochromatic transmission tomography
For practitioners of gamma-ray tomography, this work highlights a previously overlooked non-linearity and provides a method to correct it, leading to better image quality.
The paper demonstrates that monochromatic transmission tomography is non-linear when sources and detectors are not point-like, and shows that accounting for this non-linearity improves reconstructions over the linear approximation in both simulations and experimental gamma-ray tomography.
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.