Morotti, Elena (2018) Reconstruction of 3D X-ray tomographic images from sparse data with TV-based methods. [Ph.D. thesis]
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This dissertation presents efficient implementations of iterative X-rays image reconstruction methods for the specific case of three-dimensional tomographic imaging from subsampled data. When a complete projection dataset is not available, the linear system describing the so-called Sparse Tomography (SpCT) is underdetermined, hence a Total Variation (TV) regularized model is considered. The resulting optimization problem is solved by a Scaled Gradient Projection algorithm and a Fixed Point method. They both are accelerated by effective strategies, specifically tuned for a SpCT framework where fast reconstructions must be provided in short run time, facing a very large size problem. Good results on digital simulations attest the reliability of the model-based approach and of the proposed schemes. Accurate reconstructions from real medical datasets are also achieved in few iterations, confirming the feasibility of the proposed approaches to sparse tomographic imaging.
Questa tesi propone l'implementazione efficiente di due metodi iterativi per la ricostruzione di immagini tridimensionali di tomografia a raggi X, nel caso specifico in cui il volume debba essere ottenuto da dati sottocampionati. Quando le proiezioni non possono essere acquisite completamente, la risultante
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