Massaneda Clares, Francesc XavierViedma Gordillo, Diego2025-07-182025-07-182025-01-14https://hdl.handle.net/2445/222358Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2025, Director: Francesc Xavier Massaneda ClaresThis work explores the mathematical foundations and practical applications of Computerized Tomography (CT) within the context of medical imaging. By combining analytical concepts, we examine the process of generating cross-sectional images from X-ray data. The focus is placed on the properties of the Radon transform, including its relation to Fourier transforms, uniqueness theorems, and inversion formulas. Reconstruction algorithms, such as the filtered backprojection and the gridding method, are analyzed and computationally implemented, with performance evaluated using the Shepp-Logan phantom, a benchmark model for clinical image reconstruction. Additionally, we explore modern alternative geometries designed for enhanced efficiency. Beyond medical imaging, the broader implications of CT are discussed, illustrating how mathematical concepts drive transformative technological advancements.57 p.application/pdfengcc-by-nc-nd (c) Diego Viedma Gordillo, 2025http://creativecommons.org/licenses/by-nc-nd/3.0/es/Tomografia (Matemàtica)Transformacions integralsImatges mèdiquesAnàlisi de FourierTreballs de fi de grauTomography (Mathematics)Integral transformsImaging systems in medicineFourier analysisBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess