Missing wedge computed tomography by iterative algorithm DIRECTT

Summary A strategy to mitigate typical reconstruction artefacts in missing wedge computed tomography is presented. These artefacts appear as elongations of reconstructed details along the mean direction (i.e. the symmetry centre of the projections). Although absent in standard computed tomography applications, they are most prominent in advanced electron tomography and also in special topics of X‐ray and neutron tomography under restricted geometric boundary conditions. We investigate the performance of the DIRECTT (Direct Iterative Reconstruction of Computed Tomography Trajectories) algorithm to reduce the directional artefacts in standard procedures. In order to be sensitive to the anisotropic nature of missing wedge artefacts, we investigate isotropic substructures of metal foam as well as circular disc models. Comparison is drawn to filtered backprojection and algebraic techniques. Reference is made to reconstructions of complete data sets. For the purpose of assessing the reconstruction quality, Fourier transforms are employed to visualize the missing wedge directly. Deficient reconstructions of disc models are evaluated by a length‐weighted kernel density estimation, which yields the probabilities of boundary orientations. The DIRECTT results are assessed at different signal‐to‐noise ratios by means of local and integral evaluation parameters. Lay description Common understanding of computed tomography (CT) by X‐rays in everyday life mostly relates to medical diagnostics. Usually it provides brilliant images (tomograms) from inside the human body, invisible for our eyes. For X‐rays the body is transparent and a series of shadow images is the measured input for CT. Tomograms are not readily obtained, but they have to be computed by sophisticated procedures. Usually all data are employed at once in order to gain a 3D tomogram (hundreds of image slices). A complete set of viewing angles spanning at least half a circle is required for good image quality. However, in dedicated applications in life science or technological quality assurance such data sets might be incomplete as certain viewing angles are not accessible (limited view). Consequently, the (reconstructed) image suffers from strong streak disturbances, which characterise the so‐called missing wedge problem. In our new approach this problem is attacked by the alternative computing concept DIRECTT. Put simply, the desired result is not gained at once, but the truth is approached step by step. In