An efficient computational approach to model statistical correlations in photon counting x‐ray detectors

Purpose: To introduce and evaluate an increment matrix approach (IMA) describing the signal statistics of energy‐selective photon counting detectors including spatial–spectral correlations between energy bins of neighboring detector pixels. The importance of the occurring correlations for image‐based material decomposition is studied. Methods: An IMA describing the counter increase patterns in a photon counting detector is proposed. This IMA has the potential to decrease the number of required random numbers compared to Monte Carlo simulations by pursuing an approach based on convolutions. To validate and demonstrate the IMA, an approximate semirealistic detector model is provided, simulating a photon counting detector in a simplified manner, e.g., by neglecting count rate‐dependent effects. In this way, the spatial–spectral correlations on the detector level are obtained and fed into the IMA. The importance of these correlations in reconstructed energy bin images and the corresponding detector performance in image‐based material decomposition is evaluated using a statistically optimal decomposition algorithm. Results: The results of IMA together with the semirealistic detector model were compared to other models and measurements using the spectral response and the energy bin sensitivity, finding a good agreement. Correlations between the different reconstructed energy bin images could be observed, and turned out to be of weak nature. These correlations were found to be not relevant in image‐based material decomposition. An even simpler simulation procedure based on the energy bin sensitivity was tested instead and yielded similar results for the image‐based material decomposition task, as long as the fact that one incident photon can increase multiple counters across neighboring detector pixels is taken into account. Conclusions: The IMA is computationally efficient as it required about 10 2 random numbers per ray incident on a detector pixel instead of an estimated 10 8 random numbers per ray as Monte Carlo approaches would need. The spatial–spectral correlations as described by IMA are not important for the studied image‐based material decomposition task. Respecting the absolute photon counts and thus the multiple counter increases by a single x‐ray photon, the same material decomposition performance could be obtained with a simpler detector description using the energy bin sensitivity.