Theoretical Framework for the Dual-Energy Cone-Beam CT Noise-Power Spectrum, NEQ, and Tasked-Based Detectability Index

The optimization of dual-energy computed tomography (DE-CT) is challenged by the lack of a theoretical foundation for image quality. This work reports a cascaded systems analysis model that was used to derive signal and noise propagation in DE-CBCT in prevalent Fourier metrics such as the noise-power spectrum (NPS) and noise-equivalent quanta (NEQ). The model was validated in comparison to measurements of the 3D NPS and NEQ in DE-CBCT images acquired using an experimental imaging bench. Task-based detectability index was derived using DE-NPS and NEQ as an objective function in optimizing DE imaging parameters such as the dose allocation factor (D-A) and kVp pair. The resulting dose allocation optimization is in agreement with the practice of assigning more dose to the high-energy image (D-A < 0.5), and the model provides a quantitative basis for examining the optimal dose allocation as a function of total dose, kVp pair, the presence of electronics noise, and the imaging task. An example optimization is shown for a breast tumor detection task. Using DE decomposition to cancel fibroglandular tissue (rendering a DE-CBCT image of breast tumor against an adipose tissue background) and assuming a total dose of 15mGy, the optimal kVp pair is identified at [45, 105] kVp with D-A=0.46. The model is sufficiently general for applications beyond this example, demonstrating utility in the optimization in a broad range of imaging parameters. The model provides a new, valuable framework for understanding the theoretical limits of DE-CBCT imaging performance and maximizing image quality while minimizing radiation dose.