Lecture 12 Computed Tomography George Yuan Hong Kong University of Science and Technology Fall 2010
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Outline • • • • • •
Introduction X-ray Fundamentals Image Reconstruction CT Performance Metrics Direct Conversion Detector In-direct Conversion Detector
© George Yuan, HKUST
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X-ray Radiography
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Tomography • A technique of x-ray photography by which a single plane is photographed, with the outline of structures in other planes eliminated
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Off-focal Plane
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1st-Generation CT
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2nd-Generation CT
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3rd-Generation CT
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Centrifugal Force a r 2
2 frames/sec, 0.75m radius
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4th-Generation CT
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5th-Generation CT
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Outline • • • • • •
Introduction X-ray Fundamentals Image Reconstruction CT Performance Metrics Direct Conversion Detector In-direct Conversion Detector
© George Yuan, HKUST
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X-ray • E = h = hc/ = 1.24×103eV×nm/ – Soft x-ray 10nm (124eV)~0.1nm (12.4keV) – Hard x-ray 0.1nm(12.4keV)~0.01nm(1 24keV) © George Yuan, HKUST
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X-ray Generation 1 • Electron approaches close to the nucleus – Bremsstrahlung radiation – Continuous – I~Z2z4e6/m2: electron is 3million times more efficient
• Electron collides the inner shell electron – Outer shell electron fills – Characteristic radiation © George Yuan, HKUST
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X-ray Generation 2 • Electron collides a nucleus – Bremsstrahlung radiation
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X-ray Interaction 1 • Photoelectric effect – Photon absorbed by an electron
• Compton effect – Deflection – Low-energy backscattered
• Coherent scattering – Oscillating electrons transmit same EM wave © George Yuan, HKUST
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X-ray Interaction 2
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X-ray Absorption I I 0 e r L I 0 e L
• Beer-Lambert law • Water and soft tissue are similar • Iodine has much higher attenuation • Bone has high attenuation © George Yuan, HKUST
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CT Number water CT number 1000 water
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Hounsfield unit (HU) Water 0HU air -1000HU Soft tissues: -100HU~60HU Cortical bone: 250HU~1000HU
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Outline • • • • • •
Introduction X-ray Fundamentals Image Reconstruction CT Performance Metrics Direct Conversion Detector In-direct Conversion Detector
© George Yuan, HKUST
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Line Integrals
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Sampling Geometry
• Parallel projection • Fan-beam projection • Cone-beam projection – Multiple fan-beam © George Yuan, HKUST
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Sinogram
• Point object: x’ = r·cos(-) • Collections of sines © George Yuan, HKUST
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Reconstruction Example
• N×N small elements need N2 equations • More equations than unknowns © George Yuan, HKUST
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Iterative Reconstruction
• No a priori knowledge: assume uniform along the ray path © George Yuan, HKUST
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Fourier Slice Theorem • The Fourier transform of a parallel projection of an object f(x,y) obtained at angle t equals a line in a 2D Fourier transform of f(x,y) taken at the same angle
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Filtered Back-Projection • Sampling pattern from the projection Fourier transformation is polar coordinates. • Can’t perform direct Cartesian inverse transform
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Outline • • • • • •
Introduction X-ray Fundamentals Image Reconstruction CT Performance Metrics Direct Conversion Detector In-direct Conversion Detector
© George Yuan, HKUST
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In-Plane Resolution • lp/mm: line pairs per millimeter – 10 lp/cm, 0.5 mm-wide teeth
• X-ray film: 4-20 lp/mm • CT: 0.5-2 lp/mm
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Limiting Resolution • Point spread function: PSF, spatial • Modulation transfer function: MTF, spectral • Limiting frequency, limiting resolution – 0% MTF – 10%, 50%
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Slice Sensitivity Profile • Resolution in the z direction • FWHM: full width at half maximum • FWTM: full width at tenth maximum
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Low-Contrast Resolution • Low-contrast detectability: LCD • Resolution depends on contrast and noise • Low contrast phantom
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CT System
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X-ray Tube
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Outline • • • • • •
Introduction X-ray Fundamentals Image Reconstruction CT Performance Metrics Direct Conversion Detector In-direct Conversion Detector
© George Yuan, HKUST
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Direct Conversion Detector
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Outline • • • • • •
Introduction X-ray Fundamentals Image Reconstruction CT Performance Metrics Direct Conversion Detector In-direct Conversion Detector
© George Yuan, HKUST
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In-direct Conversion Detector
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Scintillating Material
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A-Si Flat-Panel Detector
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A-Si Flat-Panel Detector
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A-Se Avalanche Detector
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CCD Detector
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CMOS Detector
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Wide Dynamic Range
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Low-Capacitive Photodiode
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Noise
Reset phase
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High-gain phase
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CMOS Detector
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CMOS Current-Mode Detector
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Pixel Circuit
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Implementation
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CT/SPECT Detector • SPECT: single photon emission computed tomography • -ray emitting radio-labeled tracers
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Detector Architecture
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Noise Sources
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Charge Sensing Amplifier
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References 1. 2. 3. 4. 5. 6.
7. 8.
9. 10.
J. Hsieh, Computed Tomography: principles, design, artifacts, and recent advances, 2nd edition, SPIE Press, USA, 2009 A. Sultana, M. Wronski, K. Karim, and J. Rowlands, “Digital X-ray imaging using avalanche a-Se photoconductor”, IEEE Sensors Journal, pp. 347-352, Feb. 2010 J. Rocha, and S. Lanceros-Mendez, “3D modeling of scintillator-based X-ray detectors”, IEEE Sensors Journal, Vol. 6, pp. 1236-1242, Oct. 2006 A. Nassalski, M. Kapusta, T. Batsch, D. Wolski, D. Mockel, W. Enghardt, and M. Moszynski, “Comparative study of scintillators for PET/CT detectors”, IEEE Trans. Nuclear Science, Vol. 54, pp. 3-10, Feb. 2007 A. Sultana, K. Karim, and J. Rowlands, “Selenium-based amorphous silicon flat-panel digital X-ray imager for protein crystallography”, Can. J. Elect. Comput. Eng., Vol. 33, pp. 139-143, Sum./Fal. 2008 F. Ouandji, E. Potter, W. Chen, Y. Li, D. Tang, and H. Liu, “Characterization of a CCD-based digital x-ray imaging system for small-animal studies: properties of spatial resolution”, Applied Optics, Vol. 41, pp. 24202427, May 2002 H. Hiriyannaiah, “X-ray computed tomography for medical imaging”, IEEE Signal Processing Magazine, pp. 42-59 , Mar. 1997 R. Steadman, F. Morales, G. Vogtmeier, A. Kemna, E. Oezkan, W.Brockherde, and B. J. Hosticka, “A CMOS photodiode array with in-pixel data acquisition system for computed tomography,” IEEE J.Solid-State Circuits, vol. 39, no. 7, pp. 1034–1043, Jul. 2004 R. Steadman, G. Vogtmeier, A. Kemma, S. Quossai, and B. Hosticka, “A high dynamic range current-mode amplifier for computed tomography”, IEEE J.Solid-State Circuits, vol. 41, no. 7, pp. 1615-1619, Jul. 2006 C. Boles, B. Boser, B. Hasegawa, and J. Heanue, “A multimode digital detector readout for solid-state medical imaging detectors”, IEEE J.Solid-State Circuits, vol. 33, no. 5, pp. 733-742, May. 1998
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