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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2


Fan beam scan

From

: W. A

. Kal

ende

r; C

ompu

ted

Tom

ogra

phy,

Pub

licis

, 200

5

3


Fan beam reconstruction geometry

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From Cho et al (1993), Foundations of Medical Imaging, Wiley

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3


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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Reconstruction methods

6/x

From

Cho

et a

l (19

93),

Foun

datio

ns o

f Med

ical

Imag

ing,

Wile

y

6

4


Fourier slice theorem

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Reconstruction in the Fourier domain

8/x

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

8

5


MR scanner

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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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10

6

Center for Fast Ultrasound Imaging, Department of Health TechnologyTechnical University of Denmark 11/x

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Gradient coils

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7


MR measurement and reconstruction

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MR images

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MR images

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MR overview image

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9


Algebraic reconstruction

17/x

From

: W. A

. Kal

ende

r; C

ompu

ted

Tom

ogra

phy,

Pub

licis

, 200

5

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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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Positron Emission Tomography

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From Prince & Links, 2015

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ImagesCT PET PET/CT

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HRRT PET scanner with ART

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HRRTscanner

ConventionalPET scanner

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Reconstruction methods

22/x

From

Cho

et a

l (19

93),

Foun

datio

ns o

f Med

ical

Imag

ing,

Wile

y

22

12


Exercise 5 - Shepp-Logan phantom

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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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Exercise 5: Image processing

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From

: W. A

. Kal

ende

r; C

ompu

ter T

omog

raph

y, P

ublic

is, 2

005

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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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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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reconstruction ct pet mr ver 2020 - courses.healthtech.dtu.dk

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