Material-specific transfer function model and SNR in CT

Abstract

This study presents an analytical model for the edge spread function (ESF) of a clinical CT system that allows reliable fits of noisy ESF data. The model was used for the calculation of the material-specific transfer function TF and an estimation of the signal transfer and the signal-to-noise ratio (SNR) in 2D. Images of the Catphan phantom were acquired with a clinical Siemens Somatom Sensation Cardiac 64 CT scanner combining four different x-ray tube outputs (40, 150, 250 and 350 mAs) with four different reconstruction filters, which covered the range from very smooth (B10s) to very sharp (B70s). The images of the high- and mid-contrast cylinders of the phantom’s ‘Geometry and Sensitometry’ module (air, Teflon, Delrin and PMP) were used to sample material-specific ESF curves. The ESF curves were fitted with the analytical model we developed based on a linear combination of Boltzmann and Gaussian functions. The analytical model of the ESF was used to obtain the Fourier-based material-specific transfer function TF, as well as the spatial-domain point spread function (PSF). TF was subsequently used to estimate the signal transfer, which was compared to the actual reconstructed image of a 3.0 mm diameter Teflon pin. The noise power spectrum (NPS) was calculated from images of a uniform water phantom under the same technique parameters. The task-specific SNR was calculated for all technique parameters from the model-based TF, the measured NPS and simulated 3 mm diameter disc signals modeling the aforementioned materials. Bootstrapping was performed to estimate the standard deviation of the TF and the SNR. The analytical model we developed accurately captured the features of the CT ESF data. The coefficient of determination R2, a metric that describes the goodness of the fit, had a median value of 0.9995, and decreased for low tube output, low contrast and the sharp reconstruction filter. Our analysis showed that ESF, PSF and TF depended not only on the reconstruction filter, but also on the tube output and the material of the cylinders. For B40s and B70s, the TF of Delrin was significantly higher than the TF of other materials in the frequency range of 0.4–0.9 mm−1. The estimated signal transfer agreed well with the actual reconstructed image of the Teflon pin. For the technique parameters we used the SNR values ranged between [64, 320], [64, 281], [37, 137] and [33, 117] for air, Teflon, Delrin and PMP respectively. While for high-contrast materials the smoothest reconstruction filter resulted in the highest SNR, for mid-contrast materials the standard filter gave the best results. The presented approach provides an accurate, analytical description of the material-specific ESF, PSF and TF as well as an estimate of the signal transfer. The transfer function TF together with the NPS and simulated signals allow the calculation of a task-specific SNR.