Abstract. We present a flexible framework for robust computed tomography (CT) reconstruction with a specific emphasis on recovering thin 1D
and 2D manifolds embedded in 3D volumes. To reconstruct such structures at resolutions below the Nyquist limit of the CT image sensor, we
devise a new 3D structure tensor prior, which can be incorporated as
a regularizer into more traditional proximal optimization methods for
CT reconstruction. As a second, smaller contribution, we also show that
when using such a proximal reconstruction framework, it is beneficial to
employ the Simultaneous Algebraic Reconstruction Technique (SART)
instead of the commonly used Conjugate Gradient (CG) method in the
solution of the data term proximal operator. We show empirically that
CG often does not converge to the global optimum for tomography problem even though the underlying problem is convex. We demonstrate that
using SART provides better reconstruction results in sparse-view settings
using fewer projection images. We provide extensive experimental results
for both contributions on both simulated and real data. Moreover, our
code will also be made publicly available.