Comparison of five one-step reconstruction algorithms for spectral CT

International audienceOver the last decade, dual-energy CT scanners have gone from prototypes to clinically available machines, and spectral photon counting CT scanners are following. They require a specific reconstruction process, consisting of two steps: material decomposition and tomographic reconstruction. The two steps can be done 5 separately in either order, but in both cases, some information is lost along the way. As an alternative, "one-step inversion" methods have been proposed, which perform decomposition and reconstruction simultaneously. For most CT applications, reconstruction time is critical for practical usability, and one-step methods are typically 10 slower than their two-step counterparts. The goal of this paper is to provide an independent comparison of five one-step inversion algorithms, focused mainly on convergence speed, but also on memory footprint, stability, and ease of use. We adapted and implemented a Bayesian method which uses non-linear conjugate 15 gradient for minimization [1], three methods based on quadratic surrogates [2, 3, 4], and a primal-dual method based on MOCCA, a modified Chambolle-Pock algorithm [5]. Experiments were performed on both simulated and real data. Some of these methods can be accelerated by using µ-preconditioning, i.e. by performing 20 all internal computations not with the actual materials the object is made of, but with carefully chosen linear combinations of those. In this paper, we also evaluate the impact of three different µ-preconditioners on convergence speed. Our results show that the method of Mechlem et al. [4] is much faster than the others, while 25 being only slightly less stable and more complex: it requires less than 100 iterations, versus several thousands for other methods. It seems to be the only viable candidate for implementation into a real multi-energy scanner