Quantitative X-ray fluorescence imaging of gold nanoparticles using joint L1 and total variation regularized reconstruction.

Background: This work proposed a joint L1 and total variation (TV) regularized reconstruction method for X-ray fluorescence tomography (XFT), and investigated the performance of this method in quantitative imaging of gold nanoparticles (GNPs).

Methods: We developed a dual-modality XFT/CT imaging system which consisted of a benchtop X-ray source, a translation/rotation stage, a silicon drift detector for X-ray fluorescence (XRF) detection, and a flat panel detector for transmission X-ray detection. A pencil-beam collimator was 3D printed with steel and employed in sample excitation. The sensitivity of the XFT imaging system was determined by imaging water phantoms with multiple inserts containing GNP solutions of various concentrations (0.02-0.16 wt.%). A joint L1 and total variation (TV) regularized algorithm was developed for XFT reconstruction, where the L1 regularization was used to reduce image artifacts and the TV regularization was used to preserve the shape of targets. Nonlinear conjugate gradient (NCG) descent algorithm with backtracking line search was adopted to solve the reconstruction problem. We compared the L1 + TV regularization method with filtered back projection (FBP), maximum likelihood expectation maximization (ML-EM), L1 regularization, and TV regularization methods. Contrast-to-noise ratio (CNR), Dice similarity coefficient (DSC) and localization error (LE) metrics were used to compare the performance of different methods. The CT and XFT imaging doses were also measured using EBT2 radiochromic films.

Results: The 3D printed pencil-beam collimator shaped an excitation beam with a 2 mm full width at half maximum at the imaging isocenter. Based on the phantom imaging experiments, the joint L1 and TV regularization method performed better than FBP, ML-EM, L1 regularization and TV regularization methods, with higher localization accuracy (offset <0.6 mm), CNR and DSC values. Compared with CT, XFT with L1 + TV regularized reconstruction demonstrated higher sensitivity in GNP imaging, and could detect GNP at a concentration of 0.02 wt.% or lower. Moreover, there existed a significant linear correlation (R>0.99) between the reconstructed and true GNP concentration. The estimated XFT imaging dose is about 41.22 cGy under current setting.

Conclusions: The joint L1 + TV regularized reconstruction algorithm performed better in noise suppression and shape preservation. Using the L1 + TV regularized reconstruction, the XFT system is able to localize GNP targets with submillimeter accuracy and quantify GNP distribution at a concentration of 0.02 wt.% or lower.