An algorithm for modeling non-linear system effects in iterative CT reconstruction

With continued development and clinical deployment of iterative algorithms for CT, there remain many open questions about the best way to model various physical effects that degrade CT images, including geometric effects (finite sized detectors and sources), spectral effects due to the use of polychromatic spectra, scattered radiation, and noise. In this paper, we focus on the question of geometric modeling. Some recent investigations have concluded that geometric modeling may be unnecessary, with simple point source and point detector models yielding good results as measured near the isocenter of images. We further investigate this question in the present work, paying particular attention to peripheral image quality, where we find the effects of modeling to be more significant than at the isocenter. We also seek to evaluate the question of whether nonlinear modeling, which more closely captures the way CT data are acquired, offers any advantage over the traditional linear modeling used in iterative CT algorithms. In order to more accurately model the averaging in the transmitted intensity domain, we derive an update equation using separable paraboloidal surrogates (SPS) that is able to model a finite source, finite detectors, and data acquired over a small angular trajectory. We model these effects by incorporating many "beamlets" into the imaging model. In this work, we compare reconstructions made with additional modeling and without modeling in an SPS algorithm. We find that while modeling geometry makes a significant impact on the reconstructed image, a non-linear model may not be worth the additional computational cost.