Scattering Noise Model Enhanced EM-TV Algorithm for Benchtop X-ray Fluorescence Computed Tomography Image Reconstruction

Current benchtop x-ray fluorescence computed tomography (XFCT) devices, which use x-ray tubes to stimulate x-ray fluorescence (XRF) photons, suffer from the contamination of Compton scatter background produced by the polychromatic incident beam. The conventional maximum-likelihood expectation-maximization (ML-EM) algorithm only considers the noise model of the XRF signal, which results in high statistical noise in reconstructed images caused by scattered photons. In this study, we proposed a scattering noise model enhanced EM-TV algorithm for benchtop XFCT image reconstruction in order to reduce the noise of scatter background and improve the sensitivity of XFCT images. The statistical noise of scattered photons was considered in the likelihood function and the EM iteration step was modified correspondingly to suppress the statistical noise caused by Compton scattered photons. The robustness of the EM iteration was improved by applying the reweighted total variation (TV) norm as the penalty function. Numerical simulations and imaging experiments of a PMMA phantom consisting of gadolinium (Gd) solutions were performed to validate the proposed algorithm. The phantom was irradiated by a cone-beam polychromatic source and the projection was recorded by a linear-array photon counting detector. For comparison, the XFCT images of Gd were reconstructed using different algorithms. Results indicate that compared with the conventional ML-EM algorithm, the proposed algorithm can obtain XFCT images with lower background noise and higher contrast, which may further improve the sensitivity and image performance of current benchtop XFCT systems.