reconstruction ct pet mr ver 2020 - courses.healthtech.dtu.dk
Transcript of reconstruction ct pet mr ver 2020 - courses.healthtech.dtu.dk
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Center for Fast Ultrasound ImagingDepartment of Electrical Engineering
Reconstruction in CT and relation to other imaging modalities
Jørgen Arendt Jensen
November 2, 2020
Center for Fast Ultrasound Imaging, Build 349Department of Electrical EngineeringTechnical University of Denmark
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Reconstruction - outline
• Fan-beam geometry and reconstruction
• Overview of other reconstruction methods– In the Fourier domain – MR scanning– Algebraic reconstruction
• PET and PET/CT scanning
• Hints for Exercise 5 today
• Reading material: Prince & Links chapter 6 & 9
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Fan beam scan
From
: W. A
. Kal
ende
r; C
ompu
ted
Tom
ogra
phy,
Pub
licis
, 200
5
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Fan beam reconstruction geometry
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From Cho et al (1993), Foundations of Medical Imaging, Wiley
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Fan-beam reconstruction algorithm
!𝑓 𝑥, 𝑦 = '!
"#𝑤" ['
$%!
%!𝑤&𝑝' 𝛽 𝑔 𝛽( − 𝛽 𝑑𝛽]𝑑𝛼
•Weight 1: 𝑤! = 𝑅" cos 𝛽
•Weight 2: 𝑤# =!#$
!%!
•Filter: 𝑔 𝛽 = &'() & ℎ 𝛽 , ℎ(𝛽)↔ |𝑓|
•Definition of variables on previous slide
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Reconstruction methods
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From
Cho
et a
l (19
93),
Foun
datio
ns o
f Med
ical
Imag
ing,
Wile
y
6
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Fourier slice theorem
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Reconstruction in the Fourier domain
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From
Mag
nuss
on (1
993)
, Li
nogr
aman
d ot
her d
irect
Fou
rier m
etho
ds
for t
omog
raph
ic re
cons
truct
ion,
Lin
dköp
ing
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
MR scanner
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Magnetic Resonance (MR) scanning
Larmor frequency:
w0 = g B0
g – Gyromagnetic ratio, 42.58 MHz/Tesla
B0 – Magnetic field in TeslaTypically 1.5 – 3 T
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From Cho et al (1993), Foundations of Medical Imaging, Wiley
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark 11/x
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Gradient coils
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From Cho et al (1993), Foundations of Medical Imaging, Wiley
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
MR measurement and reconstruction
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
MR images
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
MR images
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
MR overview image
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Algebraic reconstruction
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From
: W. A
. Kal
ende
r; C
ompu
ted
Tom
ogra
phy,
Pub
licis
, 200
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
PET and PET/CT scanningPositron Emission Tomography
– Radioactive FDG-18 injected
– Radioactive decay gives positron
– Annihilation with electron yields two 511 keV photons (gamma rays)
– Detected along line of response
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Positron Emission Tomography
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From Prince & Links, 2015
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
ImagesCT PET PET/CT
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
HRRT PET scanner with ART
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HRRTscanner
ConventionalPET scanner
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Reconstruction methods
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From
Cho
et a
l (19
93),
Foun
datio
ns o
f Med
ical
Imag
ing,
Wile
y
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Exercise 5 - Shepp-Logan phantom
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Hounsfield units
From
: W. A
. Kal
ende
r; C
ompu
ted
Tom
ogra
phy,
Pub
licis
, 200
5
Note that the in-vivo projected data on the website is off-set by 1000 HU (-1000 is off-set to 0)
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Exercise 5: Image processing
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
From
: W. A
. Kal
ende
r; C
ompu
ter T
omog
raph
y, P
ublic
is, 2
005
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Exercise 5 about Image processing
1. Show Shepp-Logan phantom images.2. Shepp-Logan phantom gray scale mapping.3. Clinical images of the brain and its gray scale mapping.4. Make a two-dimensional Fourier transform of the sh black
image, and make a mesh plot of the amplitude spectrum with the command mesh. Plot the spectrum with the correct spatial frequency axis. Study the symmetry relations for the Fourier transform.
5. Make a low-pass filter with a circularly symmetric transfer function that removes all frequencies above a value of 116 m−1.
6. Use an edge enhancement filter given as [-1 -1 -1; -1 9 -1; -1 -1 -1] to enhance the edges in the image sh black.
7. Try the above mentioned image processing on the clinical images downloaded previously.
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Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark
Reconstruction summary
• Filtered backprojection algorithm and choices
• Fan-beam geometry and reconstruction• Overview of other reconstruction
methods ––MR, PET, PET/CT
• Advise for the assignments
• Next time: Algebraic reconstruction with Professor Per Christian Hansen, DTU Compute
• Reading material: –Prince & Links chapter 6-9, 12 & 13
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