Practical approaches to approximating MTF and NPS in CT with an example application to task-based observer studies

Purpose: To investigate two methods of approximating the Modulation Transfer Function (MTF) and Noise Power Spectrum (NPS) in computed tomography (CT) for a range of scan parameters, from limited image acquisitions.

Methods: The two methods consist of 1) using a linear systems approach to approximate the NPS for different filtered backprojection (FBP) kernels with a filter function derived from the kernel ratio of determined MTFs and 2) using an empirical fitted model to approximate the MTF and NPS. In both cases a scaling function accounts for variations in mAs and kV. The two methods of approximating the MTF/NPS are further investigated by comparing image quality figure of merits (FOM) d' and AUC calculated using approximations of the MTF/NPS and MTF/NPS that have been determined for different mAs/kV levels and reconstruction kernels.

Results: The greatest RMSE for NPS approximated for a range of mAs/kVp/convolution kernels using both methods and compared to determined NPS was 0.05 of the peak value. The RMSE for FOM with the kernel ratio method were at most 0.1 for d' and 0.01 for the AUC. Using the empirical model method, the RMSE for FOM were at most 0.02 for d' and 0.001 for the AUC.

Conclusions: The two methods proposed in this paper can provide a convenient way of approximating the MTF and NPS for use in, among other things, mathematical observer studies. Both methods require a relatively small number of direct determinations of NPS from scan acquisitions to model the NPS/MTF for arbitrary mAs and kV.