[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 reconstrucción de imagen de tomografía axial computerizada (TAC), en su modalidad model-based, prevalecen los algoritmos iterativos. Aunque los altos tiempos de reconstrucción aún son una barrera para aplicaciones prácticas, diferentes técnicas para la aceleración de su convergencia están siendo objeto de investigación, obteniendo resultados impresionantes. En esta tesis, se propone un algoritmo directo para la reconstrucción de imagen model-based. La aproximación model-based se basa en la construcción de una matriz modelo que plantea un sistema lineal cuya solución es la imagen reconstruida. El algoritmo propuesto consiste en la descomposición QR de esta matriz y la resolución del sistema por un proceso de sustitución regresiva. El coste de esta técnica de reconstrucción de imagen es un producto matriz vector y una sustitución regresiva, ya que la construcción del modelo y la descomposición QR se realizan una sola vez, debido a que cada reconstrucción de imagen supone la resolución del mismo sistema TAC para un término independiente diferente. Durante la implementación de este algoritmo aparecen varios problemas, tales como el cálculo exacto del volumen de intersección, la definición de estrategias de reducción del relleno optimizadas para matrices de modelo de TAC, o el aprovechamiento de simetrías del TAC que reduzcan el tama\~no del sistema. Estos problemas han sido detallados y se han propuesto soluciones para superarlos, y como resultado, se ha obtenido una implementación de prueba de concepto. Las imágenes reconstruidas han sido analizadas y comparadas frente a los algoritmos de reconstrucción filtered backprojection (FBP) y maximum likelihood expectation maximization (MLEM), y los resultados muestran varias ventajas del algoritmo propuesto. Aunque no se han podido obtener resoluciones altas aún, los resultados obtenidos también demuestran el futuro de este algoritmo, ya que se podrían obtener mejoras importantes en el rendimiento y la escalabilidad con el éxito en el desarrollo de mejores estrategias de reducción de relleno o simetrías en la geometría TAC. / [CAT] En la reconstrucció de imatge tomografia axial computerizada (TAC) en la seua modalitat model-based prevaleixen els algorismes iteratius. Tot i que els alts temps de reconstrucció encara són un obstacle per a aplicacions pràctiques, diferents tècniques per a l'acceleració de la seua convergència estàn siguent objecte de investigació, obtenint resultats impressionants. En aquesta tesi, es proposa un algorisme direct per a la recconstrucció de image model-based. L'aproximació model-based es basa en la construcció d'una matriu model que planteja un sistema lineal quina sol·lució es la imatge reconstruida. L'algorisme propost consisteix en la descomposició QR d'aquesta matriu i la resolució del sistema per un procés de substitució regresiva. El cost d'aquesta tècnica de reconstrucció de imatge es un producte matriu vector i una substitució regresiva, ja que la construcció del model i la descomposició QR es realitzen una sola vegada, degut a que cada reconstrucció de imatge suposa la resolució del mateix sistema TAC per a un tèrme independent diferent. Durant la implementació d'aquest algorisme sorgixen diferents problemes, tals com el càlcul exacte del volum de intersecció, la definició d'estratègies de reducció de farcit optimitzades per a matrius de model de TAC, o el aprofitament de simetries del TAC que redueixquen el tamany del sistema. Aquestos problemes han sigut detallats y s'han proposat solucions per a superar-los, i com a resultat, s'ha obtingut una implementació de prova de concepte. Les imatges reconstruides han sigut analitzades i comparades front als algorismes de reconstrucció filtered backprojection (FBP) i maximum likelihood expectation maximization (MLEM), i els resultats mostren varies ventajes del algorisme propost. Encara que no s'han pogut obtindre resolucions altes ara per ara, els resultats obtinguts també demostren el futur d'aquest algorisme, ja que es prodrien obtindre millores importants en el rendiment i la escalabilitat amb l'éxit en el desemvolupament de millors estratègies de reducció de farcit o simetries en la geometria TAC. / Iborra Carreres, A. (2015). Development of a New 3D Reconstruction Algorithm for Computed Tomography (CT) [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/59421 / TESIS

Radiomics treats images as quantitative data and promises to improve cancer prediction in radiology and therapy response assessment in radiation oncology. However, there are a number of fundamental problems that need to be solved in order to potentially apply radiomic features in clinic. The first basic step in computed tomography (CT) radiomic analysis is the acquisition of images using selectable image acquisition and reconstruction parameters. Radiomic features have shown large variability due to variation of these parameters. Therefore, it is important to develop methods to address these variability issues in radiomic features due to each CT parameter. To this end, texture phantoms provide a stable geometry and Hounsfield Units (HU) to characterize the radiomic features with respect to image acquisition and reconstruction parameters. In this project, normalization methods were developed to address the variability issues in CT Radiomics using texture phantoms. In the first part of this project, variability in radiomic features due to voxel size variation was addressed. A voxel size resampling method is presented as a preprocessing step for imaging data acquired with variable voxel sizes. After resampling, variability due to variable voxel size in 42 radiomic features was reduced significantly. Voxel size normalization is presented to address the intrinsic dependence of some key radiomic features. After normalization, 10 features became robust as a function of voxel size. Some of these features were identified as predictive biomarkers in diagnostic imaging or useful in response assessment in radiation therapy. However, these key features were found to be intrinsically dependent on voxel size (which also implies dependence on lesion volume). The normalization factors are also developed to address the intrinsic dependence of texture features on the number of gray levels. After normalization, the variability due to gray levels in 17 texture features was reduced significantly. In the second part of the project, voxel size and gray level (GL) normalizations developed based on phantom studies, were tested on the actual lung cancer tumors. Eighteen patients with non-small cell lung cancer of varying tumor volumes were studied and compared with phantom scans acquired on 8 different CT scanners. Eight out of 10 features showed high (Rs > 0.9) and low (Rs < 0.5) Spearman rank correlations with voxel size before and after normalizations, respectively. Likewise, texture features were unstable (ICC < 0.6) and highly stable (ICC > 0.9) before and after gray level normalizations, respectively. This work showed that voxel size and GL normalizations derived from texture phantom also apply to lung cancer tumors. This work highlights the importance and utility of investigating the robustness of CT radiomic features using CT texture phantoms. Another contribution of this work is to develop correction factors to address the variability issues in radiomic features due to reconstruction kernels. Reconstruction kernels and tube current contribute to noise texture in CT. Most of texture features were sensitive to correlated noise texture due to reconstruction kernels. In this work, noise power spectra (NPS) was measured on 5 CT scanners using standard ACR phantom to quantify the correlated noise texture. The variability in texture features due to different kernels was reduced by applying the NPS peak frequency and the region of interest (ROI) maximum intensity as correction factors. Most texture features were radiation dose independent but were strongly kernel dependent, which is demonstrated by a significant shift in NPS peak frequency among kernels. Percent improvements in robustness of 19 features were in the range of 30% to 78% after corrections. In conclusion, most texture features are sensitive to imaging parameters such as reconstruction kernels, reconstruction Field of View (FOV), and slice thickness. All reconstruction parameters contribute to inherent noise in CT images. The problem can be partly solved by quantifying noise texture in CT radiomics using a texture phantom and an ACR phantom. Texture phantoms should be a pre-requisite to patient studies as they provide stable geometry and HU distribution to characterize the radiomic features and provide ground truths for multi-institutional validation studies.

Dual-energy computed tomography (DECT) has shown great potential in the reduction of uncertainties of proton ranges and low energy photon cross section estimation used in radiation therapy planning. The work presented herein investigated three contributions for advancing DECT applications. 1) A linear and separable two-parameter DECT, the basis vector model (BVM) was used to estimate proton stopping power. Compared to other nonlinear two-parameter models in the literature, the BVM model shows a comparable accuracy achieved for typical human tissues. This model outperforms other nonlinear models in estimations of linear attenuation coefficients. This is the first study to clearly illustrate the advantages of linear model not only in accurately mapping radiological quantities for radiation therapy, but also in providing a unique model for accurate linear forward projection modelling, which is needed by the statistical iterative reconstruction (SIR) and other advanced DECT reconstruction algorithms. 2) Accurate DECT requires knowledge of x-ray beam properties. Using the Birch-Marshall1 model and beam hardening correction coefficients encoded in a CT scanner’s sinogram header files, an efficient and accurate way to estimate the x-ray spectrum is proposed. The merits of the proposed technique lie in requiring no physical transmission measurement after a one-time calibration against an independently measured spectrum. This technique can also be used in monitoring the aging of x-ray CT tubes. 3) An iterative filtered back projection with anatomical constraint (iFBP-AC) algorithm was also implemented on a digital phantom to evaluate its ability in mitigating beam hardening effects and supporting accurate material decomposition for in vivo imaging of photon cross section and proton stopping power. Compared to iFBP without constraints, both algorithms demonstrate high efficiency of convergence. For an idealized digital phantom, similar accuracy was observed under a noiseless situation. With clinically achievable noise level added to the sinograms, iFBP-AC greatly outperforms iFBP in prediction of photon linear attenuation at low energy, i.e., 28 keV. The estimated mean errors of iFBP and iFBP-AC for cortical bone are 1% and 0.7%, respectively; the standard deviations are 0.6% and 5%, respectively. The achieved accuracy of iFBP-AC shows robustness versus contrast level. Similar mean errors are maintained for muscle tissue. The standard deviation achieved by iFBP-AC is 1.2%. In contrast, the standard deviation yielded by iFBP is about 20.2%. The algorithm of iFBP-AC shows potential application of quantitative measurement of DECT. The contributions in this thesis aim to improve the clinical performance of DECT.