Spatio‐energetic cross‐talk in photon counting detectors: Numerical detector model (PcTK) and workflow for CT image quality assessment

Purpose The interpixel cross‐talk of energy‐sensitive photon counting x‐ray detectors ( PCD s) has been studied and an analytical model (version 2.1) has been developed for double‐counting between neighboring pixels due to charge sharing and K‐shell fluorescence x‐ray emission followed by its reabsorption (Taguchi K, et al., Medical Physics 2016;43(12):6386–6404). While the model version 2.1 simulated the spectral degradation well, it had the following problems that has been found to be significant recently: (1) The spectrum is inaccurate with smaller pixel sizes; (2) the charge cloud size must be smaller than the pixel size; (3) the model underestimates the spectrum/counts for 10–40 keV; and (4) the model version 2.1 cannot handle n ‐tuple‐counting with n > 2 (i.e., triple‐counting or higher). These problems are inherent to the design of the model version 2.1; therefore, we developed a new model and addressed these problems in this study. Methods We propose a new PCD cross‐talk model (version 3.2; Pc TK for “photon counting toolkit”) that is based on a completely different design concept from the previous version. It uses a numerical approach and starts with a 2‐D model of charge sharing (as opposed to an analytical approach and a 1‐D model with version 2.1) and addresses all of the four problems. The model takes the following factors into account: (1) shift‐variant electron density of the charge cloud (Gaussian‐distributed), (2) detection efficiency, (3) interactions between photons and PCD s via photoelectric effect, and (4) electronic noise. Correlated noisy PCD data can be generated using either a multivariate normal random number generator or a Poisson random number generator. The effect of the two parameters, the effective charge cloud diameter ( d 0 ) and pixel size ( d pix ), was studied and results were compared with Monte Carlo simulations and the previous model version 2.1. Finally, a script for the workflow for CT image quality assessment has been developed, which started with a few material density images, generated material‐specific sinogram (line integrals) data, noisy PCD data with spectral distortion using the model version 3.2, and reconstructed PCD ‐ CT images for four energy windows. Results The model version 3.2 addressed all of the four problems listed above. The spectra with d pix = 56–113 μm agreed with that of Medipix3 detector with d pix = 55–110 μm without charge summing mode qualitatively. The counts for 10–40 keV were larger than the previous model (version 2.1) and agreed with MC simulations very well (root‐mean‐square difference values with model version 3.2 were decreased to 16%–67% of the values with version 2.1). There were many non‐zero off‐diagonal elements with n ‐tuple‐counting with n > 2 in the normalized covariance matrix of 3 × 3 neighboring pixels. Reconstructed images showed biases and artifacts attributed to the spectral distortion due to the charge sharing and fluorescence x rays. Conclusion We have developed a new PCD model for spatio‐energetic cross‐talk and correlation between PCD pixels. The workflow demonstrated the utility of the model for general or task‐specific image quality assessments for the PCD ‐ CT . Note: The program (Pc TK ) and the workflow scripts have been made available to academic researchers. Interested readers should visit the website (pctk.jhu.edu) or contact the corresponding author.