Purpose: Photon-counting detectors are expected to be the next big step in the development of medical computed tomography (CT). Accurate modeling of the behavior of photon-counting detectors in both low and high count rate regimes is important for accurate image reconstruction and detector performance evaluations. The commonly used ideal nonparalyzable (delta pulse) model is built on crude assumptions that make it unsuitable for predicting the behavior of photon-counting detectors at high count rates. The aim of this work is to present an analytical count statistics model that better describes the behavior of photon-counting detectors with nonzero pulse length. Methods: An analytical statistical count distribution model for nonparalyzable detectors with nonzero pulse length is derived using tools from statistical analysis. To validate the model, a nonparalyzable photon-counting detector is simulated using Monte Carlo methods and compared against. Image performance metrics are computed using the Fisher information metric and a comparison between the proposed model, approximations of the proposed model, and those made by the ideal nonparalyzable model is presented and analyzed. Results: It is shown that the presented model agrees well with the results from the Monte Carlo simulation and is stable for varying x-ray beam qualities. It is also shown that a simple Gaussian approximation of the distribution can be used to accurately model the behavior and performance of nonparalyzable detectors with nonzero pulse length. Furthermore, the comparison of performance metrics show that the proposed model predicts a very different behavior than the ideal nonparalyzable detector model, suggesting that the proposed model can fill an important gap in the understanding of pileup effects. Conclusions: An analytical model for the count statistics of a nonparalyzable photon-counting detector with nonzero pulse length is presented. The model agrees well with results obtained from Monte Carlo simulations and can be used to improve, speed up and simplify modeling of photon-counting detectors. 

Purpose: To evaluate a proposed method to reconstruct CT numbers that accurately mimic conventional CT numbers from spectral CT data, as would have been produced by a conventional system without effects of beam hardening.

Approach: We implement the proposed method for simulated ideal and non-ideal photon counting multi-bin systems, the latter based on a photon counting Silicon detector, and compare them with a simulated ideal conventional energy integrating system with a cupping correction algorithm. We compare the systems using a mathematical phantom of a size and composition that produces severe cupping and beam hardening artefacts when imaged with a conventional system with no cupping correction.

Results: The resulting images show CT numbers that are consistently accurate for a varying range of tissues and are free of beam hardening artefacts.

Conclusions: This method could facilitate use of established rules-of-thumb regarding absolute CT numbers for various organs and conditions during the transition from conventional CTto spectral CT.

Purpose: The set of linear attenuation coefficients that belong to materials in the human body is commonly assumed to be spanned by two basis functions in the range of clinical x-ray energies, even though there is evidence that the dimensionality of this set is greater than two. It has not yet been clear that the use of a third basis function could be beneficial in absence of contrast agents.

Approach: In this work, the choice of the number of basis functions used in the basis decomposition method is studied for the task of producing an image where a third material is separated from a background of two other materials, in a case where none of the materials have a K-edge in the range of considered x-ray energies (20-140 keV). The case of separating iron from mixtures of liver and adipose tissue is studied with a simulated phantom which incorporates random and realistic tissue variability.

Results: Inclusion of a third basis function improves the quantitative estimate of iron concentration by several orders of magnitude in terms of mean squared error in the resulting image.

Conclusions: The inclusion of a third basis function in the basis decomposition is essential for the studied imaging task and could have potential application for quantitative estimation of iron concentration from material decomposed images.