Estimation of Basis Line-Integrals in a Spectral Distortion-Modeled Photon Counting Detector Using Low-Rank Approximation-Based X-Ray Transmittance Modeling: K-Edge Imaging Application

Abstract

Photon counting detectors (PCDs) provide multiple energy-dependent measurements for estimating basis line-integrals. However, the measured spectrum is distorted from the spectral response effect (SRE) via charge sharing, K-fluorescence emission, and so on. Thus, in order to avoid bias and artifacts in images, the SRE needs to be compensated. For this purpose, we recently developed a computationally efficient three-step algorithm for PCD-CT without contrast agents by approximating smooth X-ray transmittance using low-order polynomial bases. It compensated the SRE by incorporating the SRE model in a linearized estimation process and achieved nearly the minimum variance and unbiased (MVU) estimator. In this paper, we extend the three-step algorithm to K-edge imaging applications by designing optimal bases using a low-rank approximation to model X-ray transmittances with arbitrary shapes (i.e., smooth without the K-edge or discontinuous with the K-edge). The bases can be used to approximate the X-ray transmittance and to linearize the PCD measurement modeling and then the three-step estimator can be derived as in the previous approach: estimating the x-ray transmittance in the first step, estimating basis line-integrals including that of the contrast agent in the second step, and correcting for a bias in the third step. We demonstrate that the proposed method is more accurate and stable than the low-order polynomial-based approaches with extensive simulation studies using gadolinium for the K-edge imaging application. We also demonstrate that the proposed method achieves nearly MVU estimator, and is more stable than the conventional maximum likelihood estimator in high attenuation cases with fewer photon counts.

Spatio‐energetic cross‐talk in photon counting detectors: N × N binning and sub‐pixel masking

“…The goodness of the soft tissue contrast is governed by the goodness of the total counts; thus, studying counts above a single threshold was sufficient and necessary. However, the accuracy of some applications that uses spectral information such as material decomposition, beam‐hardening correction, and virtual non‐contrast‐enhanced imaging, is affected by the uncertainty of the spectral shape . The quality of data would then need to be assessed using more energy thresholds possibly with a different figure‐of‐merit.…”

Spatio-energetic cross-talk in photon counting detectors: N×N binning and sub-pixel masking

“…However, the accuracy of some applications that uses spectral information such as material decomposition, beam-hardening correction, and virtual non-contrast-enhanced imaging, is affected by the uncertainty of the spectral shape. [20][21][22][23][24][25][26] The quality of data would then need to be assessed using more energy thresholds possibly with a different figure-of-merit. We shall leave it for future work.…”

Multi‐energy inter‐pixel coincidence counters for charge sharing correction and compensation in photon counting detectors

“…A software solution is a model-based compensation algorithm. [36][37][38][39] Such algorithms can address the bias using a charge sharing model; however, they cannot eliminate the noise added by charge sharing, because it is impossible to estimate (and subtract) counts of each random noise realization. Thus, the signal-to-noise ratio of the processed data is expected to be worse than what would be achieved by PCDs without charge sharing.…”

“…A software solution is a model‐based compensation algorithm . Such algorithms can address the bias using a charge sharing model; however, they cannot eliminate the noise added by charge sharing, because it is impossible to estimate (and subtract) counts of each random noise realization.…”