Model-based pulse pileup and charge sharing compensation for photon counting detectors: A simulation study

We aim at developing a model-based algorithm that compensates for the effect of both pulse pileup (PP) and charge sharing (CS) and evaluates the performance using computer simulations.

The proposed PCP algorithm for PP and CS compensation uses cascaded models for CS and PP we previously developed, maximizes Poisson log-likelihood, and uses an efficient three-step exhaustive search. For comparison, we also developed an LCP algorithm that combines models for a loss of counts (LCs) and CS. Two types of computer simulations, slab- and computed tomography (CT)-based, were performed to assess the performance of both PCP and LCP with 200 and 800 mA, (300 µm)²  × 1.6-mm cadmium telluride detector, and a dead-time of 23 ns. A slab-based assessment used a pair of adipose and iodine with different thicknesses, attenuated X-rays, and assessed the bias and noise of the outputs from one detector pixel; a CT-based assessment simulated a chest/cardiac scan and a head-and-neck scan using 3D phantom and noisy cone-beam projections.

With the slab simulation, the PCP had little or no biases when the expected counts were sufficiently large, even though a probability of count loss (PCL) due to dead-time loss or PP was as high as 0.8. In contrast, the LCP had significant biases (>±2 cm of adipose) when the PCL was higher than 0.15. Biases were present with both PCP and LCP when the expected counts were less than 10-120 per datum, which was attributed to the fact that the maximum likelihood did not approach the asymptote. The noise of PCP was within 8% from the Cramér-Rao lower bounds for most cases when no significant bias was present. The two CT studies essentially agreed with the slab simulation study. PCP had little or no biases in the estimated basis line integrals, reconstructed basis density maps, and synthesized monoenergetic CT images. But the LCP had significant biases in basis line integrals when X-ray beams passed through lungs and near the body and neck contours, where the PCLs were above 0.15. As a consequence, basis density maps and monoenergetic CT images obtained by LCP had biases throughout the imaged space.

We have developed the PCP algorithm that uses the PP-CS model. When the expected counts are more than 10-120 per datum, the PCP algorithm is statistically efficient and successfully compensates for the effect of the spectral distortion due to both PP and CS providing little or no biases in basis line integrals, basis density maps, and monoenergetic CT images regardless of count-rates. In contrast, the LCP algorithm, which models an LC due to pileup, produces severe biases when incident count-rates are high and the PCL is 0.15 or higher.