Optimal noise control in and fast reconstruction of fan‐beam computed tomography image

Abstract

We proposed a linear approach that exploits statistically complementary information inherent in the projection data of fan‐beam computed tomography (CT) for achieving a bias‐free image‐variance reduction in fan‐beam CT. This linear approach leads to the development of infinite classes of hybrid algorithms for image reconstruction in fan‐beam CT. These hybrid algorithms are computationally more efficient and numerically less susceptible to data noise and to the effect of finite sampling than the conventional fan‐beam filtered back‐projection (FFBP) algorithm. We also developed infinite classes of generalized fan‐beam filtered back‐projection (GFFBP) algorithms, which include the conventional FFBP algorithm as a special member. We demonstrated theoretically and quantitatively that the hybrid and GFFBP algorithms are identical (or different) in the absence (or presence) of data noise and of the effect of finite sampling. More importantly, we identified the statistically optimal hybrid algorithm that may have potentially significant implication to image reconstruction in fan‐beam CT. Extensive numerical results of computer‐simulation studies validated our theoretical results.