  X-ray fluorescence computed tomography (XFCT) is a molecular imaging
technique of x-ray photons, which can be used to sense different elements or
nanoparticle (NP) agents inside deep samples or tissues. XFCT has been an
active research topic for many years. However, XFCT has not been a popular
molecular imaging tool because it has limited molecular sensitivity and spatial
resolution. To further investigate XFCT imaging, we present a benchtop XFCT
imaging system, in in which a unique pencil beam x-ray source and a ring of
x-ray spectrometers were simulated using GATE (Geant4 Application for
Tomographic Emission) software. An accelerated majorization minimization (MM)
algorithm with an L1 regularization scheme was used to reconstruct the XRF
image of Molybdenum (Mo) NP targets from the numerical measurements of GATE
simulations. With a low x-ray source output rate, good target localization was
achieved with a DICE coefficient of 83.681%. The reconstructed signal intensity
of the targets was found to be relatively proportional to the target
concentrations if detector number and placement is optimized. The MM algorithm
performance was compared with maximum likelihood expectation maximization
(ML-EM) and filtered back projection (FBP) algorithms. In the future, the
benchtop XFCT imaging system will be tested experimentally
