Lucas Parra CCNY Cit y College of New Yor k BME I5000 Biomedical Imaging Lecture 4 Computed Tomography Lucas C Parra parra ccny cuny edu some slides inspired by lecture notes of Andreas H Hilscher at Columbia University Blackboard http cityonline ccny cuny edu 1 Lucas Parra CCNY Cit y College of New Yor k Schedule 1 Introduction Spatial Resolution Intensity Resolution Noise 2 X Ray Imaging Mammography Angiography Fluoroscopy 3 Intensity manipulations Contrast Enhancement Histogram Equalization 4 Computed Tomography 5 Image Reconstruction Radon Transform Filtered Back Projection 6 Positron Emission Tomography 7 Maximum Likelihood Reconstruction 8 Magnetic Resonance Imaging 9 Fourier reconstruction k space frequency and phase encoding 10 Optical imaging Fluorescence Microscopy Confocal Imaging 11 Enhancement Point Spread Function Filtering Sharpening Wiener filter 12 Segmentation Thresholding Matched filter Morphological operations 13 Pattern Recognition Feature extraction PCA Wavelets 14 Pattern Recognition Bayesian Inference Linear classification 2 Lucas Parra CCNY Cit y College of New Yor k Biomedical Imaging Imaging Modality X Ray Single Photon Emission Comp Tomography SPECT Positron Emission Tomography PET Year R ntgen 1895 Nobel 191 Kuhl Edwards Wavelength Energy 3 100 keV 150 keV 1963 1953 Computed Axial Tomography CAT 1972 Magnetic Resonance Imaging MRI Ultrasound Inventor 1973 19401955 Brownell Sweet 150 keV Hounsfield Cormack Nobel 1979 Lauterbur Mansfield Nobel 2003 keV many GHz MHz Physical principle Measures variable tissue absorption of X Rays Radioactive decay Measures variable concentration of radioactive agent SPECT with improved SNR due to increased number of useful events Multiple axial X Ray views to obtain 3D volume of absorption Space and tissue dependent resonance frequency of kern spin in variable magnetic field Measures echo of sound at tissue boundaries CT Computed Tomography CAT Computed Axial Tomography 3 Lucas Parra CCNY Cit y College of New Yor k CT Origine Mathematical basis developed by Radon 1917 Idea popularized by Cormack 1963 First practical x ray CT scanner by Hounsfield 1971 4 Lucas Parra CCNY Cit y College of New Yor k CT then and now 1971 2000 Original axial CT image from the dedicated Siretom CT scanner Ability to see the soft tissue structures of the brain including the black ventricles for the first time Axial CT image of a normal brain using a state of the art CT system 128x128 pixel 512 x 512 pixel 1 4 hours acquisition time 0 35 sec acquisition time 1 5 days computation 1 sec computation 5 Lucas Parra CCNY Cit y College of New Yor k CT Imaging Principle Computed Axial Tomography Multiple x ray projections are acquired around the object and a 2D image is computed from those projections x y y x g x dy x y Idea Reconstruct 2D attenuation distribution x y from multiple 1D x ray projections g taken at different angles 6 Lucas Parra CCNY Cit y College of New Yor k CT Imaging Principle Computed Axial Tomography Multiple x ray projections are acquired around the object and a 2D image is computed from those projections y x Idea Reconstruct 2D attenuation distribution x y from multiple 1D x ray projections g taken at different angles 7 Lucas Parra CCNY Cit y College of New Yor k CT Imaging Principle Computed Axial Tomography Multiple x ray projections are acquired around the object and a 2D image is computed from those projections y x Idea Reconstruct 2D attenuation distribution x y from multiple 1D x ray projections g taken at different angles 8 Lucas Parra CCNY Cit y College of New Yor k CT Imaging Principle Computed Axial Tomography Multiple x ray projections are acquired around the object and a 2D image is computed from those projections y x Idea Reconstruct 2D attenuation distribution x y from multiple 1D x ray projections g taken at different angles 9 Lucas Parra CCNY Cit y College of New Yor k CT Imaging Principle Computed Axial Tomography Multiple x ray projections are acquired around the object and a 2D image is computed from those projections y x Idea Reconstruct 2D attenuation distribution x y from multiple 1D x ray projections g taken at different angles 10 Lucas Parra CCNY Cit y College of New Yor k CT Imaging Principle Computed Axial Tomography Multiple x ray projections are acquired around the object and a 2D image is computed from those projections y x Idea Reconstruct 2D attenuation distribution x y from multiple 1D x ray projections g taken at different angles 11 Lucas Parra CCNY Cit y College of New Yor k CT Simple Inversion Example Given the observed detector values how can one compute the unknown attenuation coefficients x y 4 10 4 g r 5 5 g 1 1 1 1 1 2 g 1 2 2 1 2 2 g 2 1 1 1 1 2 2 2 2 g 2 2 1 1 2 1 2 2 2 g M 1 1 0 0 0 0 1 1 M 0 5 0 5 0 0 5 0 5 0 0 5 0 5 1 1 1 2 2 1 2 2 g 1 1 g g 1 2 g 2 1 g 2 2 12 Lucas Parra CCNY Cit y College of New Yor k CT Inversion Simple Example Given the observed detector values how can one compute the unknown attenuation coefficients 1 3 4 6 4 10 4 5 5 g M Answer linear inversion M 1 g 0 1 0 2 1 1 0 2 M 1 1 2 0 1 0 2 0 1 1 3 6 4 4 g 10 4 5 5 13 Lucas Parra CCNY Cit y College of New Yor k CT CT number Hounsfield Units or CT number are units for attenuation coefficient relative to watter attenuation at water at 70keV HU 1000 water Tissue Bone Liver White matter brain Grey matter brain Blood Muscle Kidney Cerebrospinal fluid Water Fat Air water CT number HU 1000 40 60 46 43 40 10 40 30 15 0 50 100 1000 14 Lucas Parra CCNY Cit y College of New Yor k CT 1st Generation EMI Mark I Hounsfield parallel beam scanner highly collimated beam excellent scatter rejection now outdated 180o 240o rotation angle in steps of 1o Used for the head 5 min scan time 20 min reconstruction Original resolution 80x80 pixels ea 3X3 mm2 13 mm slice Translation Rotation 15 Lucas Parra CCNY Cit y College of New Yor k CT 2nd Generation Hybrid system Fan beam linear detector array 30 detectors Translation and rotation Reduced number of view angles scan time 30 s Slightly more complicated reconstruction algorithms because of fan beam projection Non parallel rays require rebinning or fan beam algorithms Translation Rotation 16 Lucas Parra CCNY Cit y College of New Yor k CT 3rd Generation Wide fan beam covers entire object 500 700 detectors ionization chamber or scintillation detector No translation required scan time seconds reduced dose motion artifacts Reconstruction time seconds Only Rotation 17 Lucas Parra CCNY Cit y College of