RESUMEN
Imaging the spatial distribution of low concentrations of metal is a growing problem of interest with applications in medical and material sciences. X-ray fluorescence emission tomography (XFET) is an emerging metal mapping imaging modality with potential sensitivity improvements and practical advantages over other methods. However, XFET detector placement must first be optimized to ensure accurate metal density quantification and adequate spatial resolution. In this work, we first use singular value decomposition of the imaging model and eigendecomposition of the object-specific Fisher information matrix to study how detector arrangement affects spatial resolution and feature preservation. We then perform joint image reconstructions of a numerical gold phantom. For this phantom, we show that two parallel detectors provide metal quantification with similar accuracy to four detectors, despite the resulting anisotropic spatial resolution in the attenuation map estimate. Two orthogonal detectors provide improved spatial resolution along one axis, but underestimate the metal concentration in distant regions. Therefore, this work demonstrates the minor effect of using fewer, but strategically placed, detectors in the case where detector placement is restricted. This work is a critical investigation into the limitations and capabilities of XFET prior to its translation to preclinical and benchtop uses.
RESUMEN
X-ray fluorescence emission tomography (XFET) is an emerging imaging modality that images the spatial distribution of metal without requiring biochemical modification or radioactivity. This work investigates the joint estimation of metal and attenuation maps with a pencil-beam XFET system that allows for direct metal measurement in the absence of attenuation. Using singular value decomposition on a simplified imaging model, we show that reconstructing metal and attenuation voxels far from the detector is an ill-conditioned problem. Using simulated data, we develop and compare two image reconstruction methods for joint estimation. The first method alternates between updating the attenuation map with a separable paraboloidal surrogates algorithm and updating the metal map with a closed-form solution. The second method performs simultaneous joint estimation with conjugate gradients based on a linearized imaging model. The alternating approach outperforms the linearized approach for iron and gold numerical phantom reconstructions. Reconstructing an (8 cm)3 object containing gold concentrations of 5 mg/cm3 and an unknown beam attenuation map using the alternating approach yields an accurate gold map (NRMSE = 0.19) and attenuation map (NRMSE = 0.14). This simulation demonstrates an accurate joint reconstruction of metal and attenuation maps, from emission data, without previous knowledge of any attenuation map.