1 Center for Fast Ultrasound Imaging Department of Electrical Engineering Radon Transform and Filtered Backprojection Jørgen Arendt Jensen October 23, 2019 Center for Fast Ultrasound Imaging, Build 349 Department of Health Technology Technical University of Denmark 1 Center for Fast Ultrasound Imaging, Department of Electrical Engineering Technical University of Denmark CT reconstruction - outline •CT scanners •Projection and Radon transform •Projection demo •Fourier slice theorem •Inverse Radon transform – filtered backprojection •Selection of filters •Filtered backprojection algorithm •Reading material: Prince & Links chapter 6 2/x 2 Center for Fast Ultrasound Imaging, Department of Electrical Engineering Technical University of Denmark Modern CT system generations From: W. A. Kalender; Computed Tomography, Publicis, 2005 3/x 3 Center for Fast Ultrasound Imaging, Department of Electrical Engineering Technical University of Denmark What do we measure? • Intensity measured by detector: • Conversion to attenuation: • Attenuation values μ are scaled relative to water: 0 ln 1 I I x - = μ 1000 ´ - = water water tissue HU μ μ μ ) exp( x I I o × - = μ 4/x 4
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Center for Fast Ultrasound ImagingDepartment of Electrical Engineering
Radon Transform andFiltered Backprojection
Jørgen Arendt Jensen
October 23, 2019
Center for Fast Ultrasound Imaging, Build 349Department of Health TechnologyTechnical University of Denmark
1
Center for Fast Ultrasound Imaging, Department of Electrical Engineering Technical University of Denmark
CT reconstruction - outline
•CT scanners•Projection and Radon transform•Projection demo