Iterative Filtered Backprojection Methods for Helical Cone-Beam CT

State-of-the-art reconstruction algorithms for medical helical cone-beam Computed Tomography (CT) are of type non-exact Filtered Backprojection (FBP). They are attractive because of their simplicity and low computational cost, but they produce sub-optimal images with respect to artifacts, resolution, and noise. This thesis deals with possibilities to improve the image quality by means of iterative techniques. The first algorithm, Regularized Iterative Weighted Filtered Backprojection (RIWFBP), is an iterative algorithm employing the non-exact Weighted Filtered Backprojection (WFBP) algorithm [Stierstorfer et al., Phys. Med. Biol. 49, 22092218, 2004] in the update step. We have measured and compared artifact reduction as well as resolution and noise properties for RIWFBP and WFBP. The results show that artifacts originating in the non-exactness of the WFBP algorithm are suppressed within five iterations without notable degradation in terms of resolution versus noise. Our experiments also indicate that the number of required iterations can be reduced by employing a technique known as ordered subsets. A small modification of RIWFBP leads to a new algorithm, the Weighted Least Squares Iterative Filtered Backprojection (WLS-IFBP). This algorithm has a slightly lower rate of convergence than RIWFBP, but in return it has the attractive property of converging to a solution of a certain least squares minimization problem. Hereby, theory and algorithms from optimization theory become applicable. Besides linear regularization, we have examined edge-preserving non-linear regularization. In this case, resolution becomes contrast dependent, a fact that can be utilized for improving high contrast resolution without degrading the signal-tonoise ratio in low contrast regions. Resolution measurements at different contrast levels and anthropomorphic phantom studies confirm this property. Furthermore, an even more pronounced suppression of artifacts is observed. Iterative reconstruction opens for more realistic modeling of the input data acquisition process than what is possible with FBP. We have examined the possibility to improve the forward projection model by (i) multiple ray models, and (ii) calculating strip integrals instead of line integrals. In both cases, for linear regularization, the experiments indicate a trade off: the resolution is improved at the price of increased noise levels. With non-linear regularization on the other hand, the degraded signal-to-noise ratio in low contrast regions can be avoided. Huge input data sizes make experiments on real medical CT data very demanding. To alleviate this problem, we have implemented the most time consuming parts of the algorithms on a Graphics Processing Unit (GPU). These implementations are described in some detail, and some specific problems regarding parallelism and memory access are discussed.