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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.
The DIRECTT (Direct Iterative REconstruction of Computed Tomography Trajectories) algorithm represents a promising alternative to conventional algorithms, such as the Filtered Backprojection (FBP) or the Algebraic Reconstruction Technique (ART), by overcoming restrictions associated with them. Such restrictions include the limited spatial resolution achieved through FBP due to Nyquist‘s sampling theorem, the inability of FBP to perform a quality reconstruction when projections are missing, and the excessive computing time needed for ART.
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.
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.
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.