Efficiently harvesting low-energy photons from silicon photon counting detectors

X-rays incident on silicon photon counting detectors (Si PCDs) may undergo Compton scattering and deposit only a few keV of energy into the sensor. These events are difficult to distinguish from electronic noise. Prior to reconstruction, the scanner must solve a hybrid estimation problem to determine attenuation, in which the lowest energy bin is corrupted by false counts, but the upper energy bins are essentially immune to electronic noise.

To efficiently estimate attenuation in this hybrid scenario. Prior authors have considered attenuation estimation with PCDs that are fully immune to electronic noise, or in energy-integrating detectors that include electronic noise, but the optimal estimator in the hybrid scenario remains unknown. The purpose of this work is to design such an attenuation estimator that reduces bias and variance in Si-PCD CT images.

We propose to use convex optimization to build a 2D-lookup table that maps counts using the lowest energy bin (containing false counts) and the upper bins (all counts grouped together as a single bin, free of false counts) to the best estimated object attenuation. The energy thresholds of the Si PCD were selected to be 6 and 10 keV using assumptions from the literature. In the regime of interest, counts are scarce, so both false counts and true counts were modeled as Poisson. Our proposed estimator was compared with three reference estimators: naive logarithm estimator and modified logarithm estimators based on Li et al. (IEEE Trans Med Img 2023) and Bushe et al. (Phys Med Biol 2023). The reference estimators were applied using either both lowest and upper bins, or using upper bins only. 20-, 30- and 40- cm water phantoms, containing two 2.6-cm bone-like inserts, were tested in simulation. We assumed a technique of 120 kVp and 833 mA without mA modulation. To avoid confounding artifacts from beam hardening, the bone-like inserts were modeled as being water-equivalent in atomic number but high density, and a water beam hardening correction was used.

The proposed estimator achieved zero average bias and the lowest variance across all phantom sizes when compared to the reference estimators. When using both energy bins for the 30-cm phantom, the logarithm, Li's, and Bushe's estimators had biases of 4, 1, and 1 HU and variances that were 7%, 5%, and 5% higher than the proposed method, respectively, in the area between the two inserts. For the 40-cm phantom, their biases increased to over 20 HU. Conversely, when using only the upper energy bins for the 30-cm phantom, the logarithm, Li's, and Bushe's estimators had biases of 4, 0, and 0 HU but with significant increase in variance to 17%, 14%, and 14% higher than our estimator, respectively, and still produced bias on the 40-cm phantom.

For Si PCDs, setting the lowest energy threshold low enough to detect at least some false counts in combination with our proposed attenuation estimator can improve dose efficiency for non-spectral imaging tasks.