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Statistical analysis of tomographic reconstruction algorithms by morphological image characteristics
(2010)
We suggest a procedure for quantitative quality control of tomographic reconstruction algorithms. Our task-oriented evaluation focuses on the correct reproduction of phase boundary length and has thus a clear implication for morphological image analysis of tomographic data. Indirectly the method monitors accurate reproduction of a variety of locally defined critical image features within tomograms such as interface positions and microstructures, debonding, cracks and pores. Tomographic errors of such local nature are neglected if only global integral characteristics such as mean squared deviation are considered for the evaluation of an algorithm. The significance of differences in reconstruction quality between algorithms is assessed using a sample of independent random scenes to be reconstructed. These are generated by a Boolean model and thus exhibit a substantial stochastic variability with respect to image morphology. It is demonstrated that phase boundaries in standard reconstructions by filtered backprojection exhibit substantial errors. In the setting of our simulations, these could be significantly reduced by the use of the innovative reconstruction algorithm DIRECTT.
Typische 'Missing Wedge'(MW)-Artefakte in Rekonstruktionen der Computertomografie können mit dem iterativen DIRECTT-Algorithmus (Direkte iterative Rekonstruktion computertomografischer Trajektorien) unterdrückt werden. Die durch fehlende Projektionswinkel bedingten MW-Restriktionen betreffen bisher nur Sonderapplikationen der Röntgen- und Neutronentomografie, müssen in der Nanometer auflösenden Elektronentomografie jedoch als Standard akzeptiert werden. Die MW-Artefakte werden besonders effektiv mit einer spezifischen DIRECTT-Prozedur partiell diskreter Zwischenlösungen beseitigt. Für die Beurteilung der Abbildungsqualität werden Rekonstruktionen von vollständigen und unvollständigen Mess- und Modell-Datensätzen erzeugt und mit Ergebnissen anderer Algorithmen (gefilterte Rückprojektion (FBP) und ART-Methoden) verglichen. Die Fourier-Transformierten der Rekonstruktionen demonstrieren die erfolgreiche Ergänzung der fehlenden Information im MW-Bereich. Die quantitative Bewertung der lokalen Rekonstruktionsqualität mit Methoden der räumlichen Statistik ergibt auch für unterschiedliche Signal-Rausch-Verhältnisse signifikante Vorteile gegenüber FBP und ART.
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 boundary orientations. The DIRECTT results are assessd at different signal-to-noise ratios by means of local and integral evaluation Parameters.