# name
Computerized tomography and the radon transform through the lens of medical imaging

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2025, Director: Francesc Xavier Massaneda Clares

# metadata.dc.description.abstract[].value
This 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.

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cc-by-nc-nd (c) Diego Viedma Gordillo, 2025

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
Computerized tomography and the radon transform through the lens of medical imaging