Joint Estimation of Metal Density and Attenuation Maps with Pencil Beam XFET

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) object containing gold concentrations of 5 mg/cm 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.