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.