medical imaging dr. mohammad dawood department of computer science university of münster germany
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
α decay β- decay β+ decay
Gamma scintigraphy PET Sinogram
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
The frequency range of sound above 20kHz is known as ultrasound
Sound spectrum
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
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-2014
Dr. Mohammad Dawood
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-2014
Dr. Mohammad Dawood
Ultrasound
- A mode (amplitude)
- B mode (brightness)
- M mode (moving)
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Ultrasound
- no functional information
- fast
- cheap
- no radiation
- portable
- no injection
- Bone / gas
- Obesity
- Operator dependence
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
x-ray source
collimator
object
detector
Reconstruction
Tomography
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Reconstruction
Radon Transformation (Line Integrals at different angles)
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Reconstruction
Inverse Radon Transformation
H: Hilbert transform
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Reconstruction
Inverse Radon Transformation
Problems with Missing data and Noise!
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
A B
D C
A+B
C+D1
A+D B+C
3
2
BA+C
D
Reconstruction
Projections
A
B+D
C
4
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
? ?
? ?
Reconstruction
Back projections
A+B
C+D1
A+B A+B
C+D C+D
2
BA+C
D
2A+B+C A+2B
C+2D A+2C+D
A+D B+C
3
3A+B+C+D
A+3B+C
A+C+3D
A+B+3C+D
A
B+D
C
4
4A+B+C+D
A+4B+C+D
A+B+C+4D
A+B+4C+D
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
4A+B+C+D
A+4B+C+D
A+B+C+4D
A+B+4C+D
Reconstruction
Back projections
3A 3B
3D 3C
- (A+B+C+D) = / (n-1) =A B
D C
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
1=Ram-Lak (ramp), 2=Shepp-Logan, 3=Cosine, and 4=Hamming
Reconstruction
FBP: Commonly used filters
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
Projections
Backproject
Filter 1D
Filter 2D
Backproject
Image
Reconstruction
Filtered Back Projection
2D/3D filtering is costly
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Medical Imaging, SS-2014
Dr. Mohammad Dawood
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-2014
Dr. Mohammad Dawood
Reconstruction
Iterative Reconstruction
Kaczmarz Method (=ART: Algebraic Reconstruction Technique)
1. Start by setting x(0) = 0
2. Compute the forward projection
3. Update the current estimate
4. Iterate steps 2,3 until the difference between new forward projection, computed in 2, and the old one is below tolerance
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