TU-F-CAMPUS-I-05: Parameterization of the Noise Power Spectrum in X-Ray Computed Tomography

Abstract

Purpose: The purpose of this work was to develop a method so that the noise power spectrum (NPS) can be approximated for arbitrary levels of mAs, from a single determination in CT. Methods: The NPS is factorized into 2 components, 1) a parameterized function representing the 1D normalized spatial frequency distribution and 2) a function to scale the magnitude of 1) for arbitrary values of mAs. The 1D NPS, normalized by image variance (NNPS), was determined for 2 FBP reconstruction kernels (smoothing and edge enhancing) for 400 mAs. The NNPS were fit to the parameterized function and a scaling function was established to approximate the image variance at arbitrary values of mAs. Using the root mean square error normalized by the maximum value (NRMSE), the NPS approximated with the factorization method was compared to the NPS determined at 5 different mAs levels. Results: The factorization resulted in a set of 7 coefficients that can be used to approximate the 1D NPS, for arbitrary levels of mAs, for the convolution kernels studied in this work. The approximated NPS (factorization) agreed well with the determined NPS for all mAs levels. The greatest NRMSE was 0.02 and was observed for the edge enhancing kernel. Conclusion: The proposed factorization method has been demonstrated as applicable for FBP reconstruction. It can be used to approximate the 1D NPS for arbitrary levels of mAs, from a single NPS determination. Furthermore, approximations of the 1D NPS can conveniently be distributed since the factorization method only used 7 coefficients in the approximation.