6720 Lecture 8_computed tomography

6720 Lecture 8_computed tomography - Lecture VIII 1. 2. 3....

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1 PHYS 6720 - Lecture VIII 1 Lecture VIII Computed Tomography 1. Hounsfield scanner as an inverse problem 2. Line integral and Fourier slice theorem 3. CT reconstruction and evolving designs 4. Image display and dose considerations PHYS 6720 - Lecture VIII 2 VIII-1 The Hounsfield Scanner • Tomography refer to 2D sectional imaging • Different from a 2D projection image of a 3D structure, tomography is achieved by selecting a 2D section of the 3D structure as an output 3D image from measured signals • Once multiple sectional images are obtained , one can readily reconstruct a 3D structure of the imaged object by “stacking up” multiple 2D images z y x Tomography PHYS 6720 - Lecture VIII VIII-1 The Hounsfield Scanner • Tomography can be realized in different ways • In confocal microscopy, sectional imaging is achieved with a hardware approach by spatially filtering out the light reflected from other sections outside of the one focused on • Requires light refraction but no inverse calculation is needed Tomography PHYS 6720 - Lecture VIII 4 VIII-1 The Hounsfield Scanner • It is very difficult for shaping x-ray beam profile without absorption loss and tomography has to be done via inverse calculation from signals to structural image • Transmitted x-ray signals are line integrated signals: Tomography (,) 0 0 (, ) e x p { (, ,) } sxy Ixy I xyzd s μ ≈− PHYS 6720 - Lecture VIII 5 VIII-1 The Hounsfield Scanner • The linear attenuation coefficient μ (x, y) can be obtained from measured signals at z as • By stacking μ (x, y) images along the z- axis, 3D reconstruction can be achieved • A scanning pencil or fan beam is used to measure transmittance in the (x, y) plane. Tomography {} 0 () () ln( ) i It isi I θ −= PHYS 6720 - Lecture VIII 6 VIII-1 The Hounsfield Scanner Tomography CT slice through the mid- abdomen showing multiple normal-appearing organs
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2 PHYS 6720 - Lecture VIII 7 VIII-1 The Hounsfield Scanner • 1917 – Radon transform concerns mapping relation between a function in a space of dimension of q and its integrated values over the hyperplanes of dimension of q-1 by J. Radon in Leipzig • When q=2 the Radon transform applies for CT • 1963 – Mathematical analysis of cross-sectional imaging by A.M. Cormack in Tuft University • 1967 – CT first conceived by G.N. Hounsfield at EMI • 1968 – CT patent by Hounsfield • 1971 – first CT scanner built to scan a brain • 1979 – Cormack and Hounsfield received Nobel prize for physiology or medicine for their work on CT and related inverse algorithms Computed Tomography – road to CT PHYS 6720 - Lecture VIII 8 VIII-1 The Hounsfield Scanner • For each pencil beam located at (t, θ ) position, we can write a linear equation about μ in each grid cell: where {i} are the set of indices of grid cell traversed by the beam with a pathlength s(i) • The total number of the linear equation are given by the number of pencil beam The first CT system – Hounsfield scanner y x θ t I 0 I(t, θ ) {} 0 (, ) () () ln( ) i It isi I θ μ −= PHYS 6720 - Lecture VIII 9 VIII-1 The Hounsfield Scanner
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This note was uploaded on 04/25/2010 for the course PHYS 6720 taught by Professor Hu during the Spring '10 term at East Carolina University .

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6720 Lecture 8_computed tomography - Lecture VIII 1. 2. 3....

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