Theoretical Prediction of Bias in Model-Based Material Decomposition

Spectral imaging has significantly improved the quantitative potential of CT compared to conventional single-energy acquisitions. However, spectral imaging is susceptible to bias, which can result in misclassification of materials and compromised quantitation accuracy. Bias quantification has traditionally relied on empirical approaches which require an ensemble of measurements and yield limited theoretical insights. In this work, we propose a theoretical framework for bias prediction in model-based material decomposition. The proposed method estimates statistical bias, which arises from the nonlinear propagation of noise during the decomposition process, and model mismatch bias, resulting from discrepancies between the assumed forward model and actual data acquisition. We validated the predicted bias with empirical measurements over a wide range of imaging conditions including spectral separation, mAs, and varying amount of mismatches in the spectral responses. Statistical bias prediction shows excellent agreement with empirical measurements except at very low levels of spectral separation and mAs. Model mismatch bias increases with increasing mismatch in spectral responses, and appears to be more sensitive to perturbations in tube potential than effective energy. The theoretical model developed in this work accurately predicts bias in a wide range of imaging conditions, facilitating the design of bias-tolerant spectral systems.