Multigrid Reconstruction Technique for X-ray Fluorescence Computed Tomography

X-ray Fluorescence Computed Tomography (XFCT) is an imaging modality aiming at mapping the elemental distribution inside the sample non-invasively. However, the self-absorption effect associated with XFCT makes the accurate reconstruction challenging. To solve this issue, reconstruction algorithms that compensates this effect have been proposed. Due to the computational complexity, almost all algorithms proposed for XFCT reconstruction have modelled XFCT in a 2D plane, which is an approximation only accurate in limited cases. In this manuscript, the limitation of modelling XFCT in a 2D plane is demonstrated. Then, an effective method for the acceleration of XFCT reconstruction in the 3D space, namely multigrid XFCT reconstruction, is proposed. Specifically, multigrid refers to the different discretization grids, on which the elemental distributions and the attenuation coefficients at the energies of fluorescence X-rays are reconstructed. Through test, it can be shown that an accurate density distribution could be obtained even if the attenuation coefficients have been reconstructed on a coarser grid. As the multigrid reconstruction strategy is independent of the methodology behind the reconstruction algorithms, it could be used to accelerate all XFCT reconstruction algorithms that simultaneously reconstruct the elemental density and the attenuation coefficients at the energies of fluorescence X-rays.