Development of a New 3D Reconstruction Algorithm for Computed Tomography (CT)

Abstract

[EN] Model-based computed tomography (CT) image reconstruction is dominated by iterative algorithms. Although long reconstruction times remain as a barrier in practical applications, techniques to speed up its convergence are object of investigation, obtaining impressive results. In this thesis, a direct algorithm is proposed for model-based image reconstruction. The model-based approximation relies on the construction of a model matrix that poses a linear system which solution is the reconstructed image. The proposed algorithm consists in the QR decomposition of this matrix and the resolution of the system by a backward substitution process. The cost of this image reconstruction technique is a matrix vector multiplication and a backward substitution process, since the model construction and the QR decomposition are performed only once, because of each image reconstruction corresponds to the resolution of the same CT system for a different right hand side. Several problems regarding the implementation of this algorithm arise, such as the exact calculation of a volume intersection, definition of fill-in reduction strategies optimized for CT model matrices, or CT symmetry exploit to reduce the size of the system. These problems have been detailed and solutions to overcome them have been proposed, and as a result, a proof of concept implementation has been obtained. Reconstructed images have been analyzed and compared against the filtered backprojection (FBP) and maximum likelihood expectation maximization (MLEM) reconstruction algorithms, and results show several benefits of the proposed algorithm. Although high resolutions could not have been achieved yet, obtained results also demonstrate the prospective of this algorithm, as great performance and scalability improvements would be achieved with the success in the development of better fill-in strategies or additional symmetries in CT geometry.; [ES] En la reconstruccion de imagen de tomografia axial computerizada (TAC), en su modalidad model-based, prevalecen los algoritmos iterativos. Aunque los altos tiempos de reconstruccion aun son una barrera para aplicaciones practicas, diferentes tecnicas para la aceleracion de su convergencia estan siendo objeto de investigacion, obteniendo resultados impresionantes. En esta tesis, se propone un algoritmo directo para la reconstruccion de imagen model-based. La aproximacion model-based se basa en la construccion de una matriz modelo que plantea un sistema lineal cuya solucion es la imagen reconstruida. El algoritmo propuesto consiste en la descomposicion QR de esta matriz y la resolucion del sistema por un proceso de sustitucion regresiva. El coste de esta tecnica de reconstruccion de imagen es un producto matriz vector y una sustitucion regresiva, ya que la construccion del modelo y la descomposicion QR se realizan una sola vez, debido a que cada reconstruccion de imagen supone la resolucion del mismo sistema TAC para un termino independiente diferente. Durante la implementacion de este algoritmo aparecen varios problemas,…