Transcript Folie 1 - uni

Medical Imaging
Dr. Mohammad Dawood
Department of Computer Science
University of Münster
Germany
Medical Imaging, SS-2011
Recap
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Medical Imaging, SS-2011
α decay
Gamma scintigraphy
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β- decay
PET
β+ decay
Sinogram
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Ultrasound / Sonography
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Medical Imaging, SS-2011
Sound spectrum
The frequency range of sound above 20kHz is known as ultrasound
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Sound wave propagation
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Medical Imaging, SS-2011
Ultrasound
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Medical Imaging, SS-2011
Ultrasound
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Ultrasound
- is produced through the conversion of electrical energy into mechanical energy
- is detected by the reverse process, by converting mechanical energy into
electrical energy.
- The transducer is a device that is both a transmitter and receiver of the
ultrasound signal and it serves a dual role in pulse echo imaging.
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Medical Imaging, SS-2011
Inge Edler und Helmut Hertz
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(1954)
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Ultrasound
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Ultrasound
Reflexion
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Scatter
Transmission
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Ultrasound
Depth
Resolution
Frequency
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Ultrasound
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Ultrasound
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Medical Imaging, SS-2011
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Medium
Speed of sound m/s
Air
331
Water
1483
Tissue
1540-1595
Liver
1549
Blood
1570
Glycerin
1923
Bones (Compact)
3600
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Medical Imaging, SS-2011
Image Reconstruction
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Medical Imaging, SS-2011
Reconstruction
Tomography
detector
x-ray source
collimator
object
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Medical Imaging, SS-2011
Reconstruction
Law of Attenuation
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Medical Imaging, SS-2011
Reconstruction
Parallel projections of a plane
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Reconstruction
y
s
Radon Transformation
f
n
r
θ
x
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Reconstruction
Radon Transformation (Line Integrals at different angles)
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Medical Imaging, SS-2011
Reconstruction
Radon Transformation
Original
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Sinogram (Radon Transform)
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Reconstruction
Inverse Radon Transformation
H: Hilbert transform
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Reconstruction
Inverse Radon Transformation
Problems with Missing data and Noise!
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Reconstruction
Filtered Back Projection
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Medical Imaging, SS-2011
Reconstruction
Filtered Back Projection
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Reconstruction
FBP: Commonly used filters
1=Ram-Lak (ramp), 2=Shepp-Logan,
3=Cosine, and 4=Hamming
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Reconstruction
Filtered Back Projection
2D/3D filtering is costly
Backproject
Filter 2D
Projections
Image
Filter 1D
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Backproject
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Reconstruction
Fourier slice theorem
Take a two-dimensional function f(r), project it onto a line, and do a
Fourier transform of that projection
Take that same function, but do a two-dimensional Fourier transform
first, and then slice it through its origin parallel to the projection line
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Medical Imaging, SS-2011
Reconstruction
Fourier Slice Theorem
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Medical Imaging, SS-2011
Reconstruction
Iterative Reconstruction
Kaczmarz Method (=ART: Algebraic Reconstruction Technique)
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Medical Imaging, SS-2011
Reconstruction
Iterative Reconstruction
Kaczmarz Method (=ART: Algebraic Reconstruction Technique)
1. Start by setting x(0) = 0
2. Compute the forward projection from the n-th estimate, i.e. b(n) = A x(n)
3. Choose i and correct the current estimate x(n)
4. Iterate steps 2,3 until the difference between new forward projection b(n),
computed in 2, and the old one is below tolerance
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Reconstruction
Iterative Reconstruction
EM (Expectation Maximization)
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