Cascaded systems analysis of the 3D NEQ for cone-beam CT and tomosynthesis

Crucial to understanding the factors that govern imaging performance is a rigorous analysis of signal and noise transfer characteristics (e.g., MTF, NPS, and NEQ) applied to a task-based performance metric (e.g., detectability index). This paper advances a theoretical framework for calculation of the NPS, NEQ, and DQE of cone-beam CT (CBCT) and tomosynthesis based on cascaded systems analysis. The model considers the 2D projection NPS propagated through a series of reconstruction stages to yield the 3D NPS, revealing a continuum (from 2D projection radiography to limited-angle tomosynthesis and fully 3D CBCT) for which NEQ and detectability index may be investigated as a function of any system parameter. Factors considered in the cascade include: system geometry; angular extent of source-detector orbit; finite number of views; log-scaling; application of ramp, apodization, and interpolation filters; back-projection; and 3D noise aliasing - all of which have a direct impact on the 3D NEQ and DQE. Calculations of the 3D NPS were found to agree with experimental measurements across a broad range of imaging conditions. The model presents a theoretical framework that unifies 3D Fourier-based performance metrology in tomosynthesis and CBCT, providing a guide to optimization that rigorously considers the system configuration, reconstruction parameters, and imaging task.