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In X-ray computed tomography (XCT), an X-ray beam of intensity I0 is transmitted through an object and its attenuated intensity I is measured when it exits the object. The attenuation of the beam depends on the attenuation coefficients along its path. The attenuation coefficients provide information about the structure and composition of the object and can be determined through mathematical operations that are referred to as reconstruction. The standard reconstruction algorithms are based on the filtered backprojection (FBP) of the measured data. While these algorithms are fast and relatively simple, they do not always succeed in computing a precise reconstruction, especially from under-sampled data. Alternatively, an image or volume can be reconstructed by solving a system of linear equations. Typically, the system of equations is too large to be solved but its solution can be approximated by iterative methods, such as the Simultaneous Iterative Reconstruction Technique (SIRT) and the Conjugate Gradient Least Squares (CGLS). This dissertation focuses on the development of a novel iterative algorithm, the Direct Iterative Reconstruction of Computed Tomography Trajectories (DIRECTT). After its reconstruction principle is explained, its performance is assessed for real parallel- and cone-beam CT (including under-sampled) data and compared to that of other established algorithms. Finally, it is demonstrated how the shape of the measured object can be modelled into DIRECTT to achieve even better reconstruction results.
The reconstruction of cone-beam computed tomography data using filtered back-projection algorithms unavoidably results in severe artefacts. We describe how the Direct Iterative Reconstruction of Computed Tomography Trajectories (DIRECTT) algorithm can be combined with a model of the artefacts for the reconstruction of such data. The implementation of DIRECTT results in reconstructed volumes of superior quality compared to the conventional algorithms.
X-ray computed tomography has many applications in materials science and non-destructive testing. While the standard filtered back-projection reconstruction of the radiographic data sets is fast and simple, it typically fails in returning accurate results from missing or inconsistent projections. Among the alternative techniques that have been proposed to handle such data is the Direct Iterative REconstruction of Computed Tomography Trajectories (DIRECTT) algorithm. We describe a new approach to the algorithm, which significantly decreases the computational time, while achieving a better reconstruction quality than that of other established algorithms.
This PhD project is part of the Marie Skłodowska-Curie International Training Network MUMMERING. The overarching goal of MUMMERING is the creation of a research tool that exploits the wealth of 3D imaging modalities applied in materials engineering.
The focus of this work is advanced reconstruction algorithms. The primary objective is the development and implementation of the DIRECTT algorithm. Due to restrictions introduced by the sample or the imaging setup during a measurement, it is not always possible to acquire data that fulfil the Nyquist sampling criterion. The DIRECTT algorithm is intended to produce reconstructions of superior quality for such cases of limited data sets, compared to those of other available algorithms, such as algebraic iterative ones. Although DIRECTT has been developed primarily for the reconstruction of volumes from data acquired by an X-ray Computed Tomography scanner, it can also be applied to the different modalities, such as laminography.
The talk describes the reconstruction principle of DIRECTT. Furthermore, reconstructions of measured data are presented and compared to reconstructions produced by other established algorithms.
Anhand von computertomografischen Messungen und Modellrechnungen werden DIRECTT-Rekonstruktionen im Vergleich mit gefilterten Rückprojektionen bewertet. Dazu wird die Rekonstruktionsqualität mittels einer zirkular erweiterten Modulations-Transfer-Funktion (MTF) und mit integralen Kenngrößen im Radon- und im Ortsraum verglichen. Zur Überprüfung der Rekonstruktionsgenauigkeit experimenteller Daten werden Mustermessungen einfacher Probengeometrien unter definierten physikalischen Bedingungen durchgeführt. Diese beinhalten die Monochromasie, die Unterdrückung von Kantenartefakten und die radiometrische Intensitätsbestimmung. Für die Qualität der Rekonstruktionen mittels DIRECTT erweisen sich sowohl unterschiedliche Rekonstruktionsfilter als auch der Verzicht auf jede Filterung als unerheblich, im Gegensatz zur gefilterten Rückprojektion.
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.
Incomplete tomographic data sets such as limited view (missing wedge) data represent a well-known challenge
for reconstruction algorithms, since they unavoidably lead to substantial image artefacts. Such data sets may
occur in industrial computed tomography of limited access (e.g. extended components, fixed objects), directional
opacity, limited sample life time or laminographic set-up. We present strategies to effectively suppress the
typical elongation artefacts (e.g. lemon-like deformed pores) by our iterative algorithm DIRECTT which offers
the opportunity to vary the versatile reconstruction parameters within each cycle. Those strategies are applied to
experimental data obtained from metallic foams as well as model simulations. Comparison is drawn to state-ofthe-
art techniques (filtered backprojection and algebraic techniques). Further reference is made to reconstructions
of complete data sets serving as gold standards. For quantitative assessment of the reconstruction
quality adapted techniques based on spatial statistics are introduced.
In order to demonstrate the challenging tasks in current R&D applications in the field of renewable energy
sources experimental neutron and electron tomographic data sets of PEM fuel cell components are processed by
an advanced version of the DIRECTT algorithm. The neutron measurements of the water distribution suffer from
several intrinsic limitations such as massive position dependent focal smearing due to the large primary neutron
beam aperture. Electron (TEM) tomography allows characterisation of nanometre sized catalyst particles but is
hampered by the following restrictions: partial opacity, a limited sector of projections (missing wedge), very few
projections, samples exceeding the detector size (region of interest) and improper angular alignment. Beyond the
capabilities of other algorithms DIRECTT proves to overcome these essential reconstruction problems, in
comparison to FBP and SIRT. Nevertheless, careful data pre-processing is an inevitable requirement in order to
fully exploit the algorithm's potentials.
Modellrechnungen mit dem CT-Algorithmus DIRECTT (Direkte iterative Rekonstruktion computertomographischer Trajektorien) haben die Vorteile gegenüber anderen Ansätzen bezüglich Ortsauflösung und Dichte gezeigt, insbesondere auch für unvollständige Datensätze wie Limited View- und Region of Interest-Szenarien. Entsprechend dem Normalfall werden hier jedoch vollständige Datensätze von Modellen und Messungen und ihre Rekonstruktionen bewertet. Die Qualität von DIRECTT wird mit der Gefilterten Rückprojektion anhand der Modulations-Transfer-Funktion (MTF) sowie integraler Kenngrößen im Radon- und im Ortsraum verglichen. Zur Überprüfung der Rekonstruktionsgenauigkeit experimenteller Daten werden Mustermessungen einfacher Probengeometrien unter definierten physikalischen Bedingungen durchgeführt. Diese betreffen Monochromasie, Unterdrückung von Kantenartefakten und radiometrische Intensitätsbestimmung mit Einkanaldetektor.