Fundamentals of
2D and 3D
CT reconstruction
Dr. Günter Lauritsch
2
Reconstructive Methods
detector
Data acquisition
system
source
object
Set of digital
projection
images
reconstruction
Tomographic slice images
algorithm
3-D image
Measured sinogram
1
3
! Introduction
! Mathematical background of 2D CT
! 2D fan beam data acquisition
! Spiral CT from 2D towards 3D
! Recent technical developments and clinical images
! Fully 3D imaging
! 3D circular cone-beam CT
4
Measuring line integrals of attenuation
coefficients µ
A x-ray beam traveling along
line j is attenuated by the
object according to Beer’s law
for the photon intensities I
collimated
x-ray source
I0

r 
I j = I 0 ⋅ exp  − ∫ µ ( r ) dl 


 line j

The photon intensities I are
preprocessed to projection
data p
p j = − ln
Ij
I0
=
r
∫ µ (r )dl
Ij
line j
Thus we have to solve a set of
integral equations for the
attenuation coefficients µ.
detector
2
5
CT-numbers of tissue in Hounsfield units (HU)
3000
Blood
Liver
60
Spleen
40
Tumor
Kidneys
Heart
Pancreas
Bone
Bladder
Adrenal
Gland
Intestine
Water
0
-100
CT - number =
Mamma
-200
µ − µ water
⋅1000
µ water
Fat
-900
Air
Lung
-1000
6
Inverse Problems
Given p (measurement data), system characterizing operator A,
find µ (object) such that p = A µ.
Usually ill-posed problems:
• A-1 does not exist
• Solution is not unique
• Solution is unstable
Task: Find reasonable approximation to solution!
Analytical methods
• First find analytical solution
µ~(x) =∫dx' k( x') ⋅ p(x−x')
with filter kernel k.
Algebraic methods
• First discretize imaging process
pi =∑ Aij µj
j
• Then discretize.
• Then invert system matrix Aij.
Typical for CT, example Radon transform
Typical for SPECT
bioelectric/-magnetic imaging
3
7
! Introduction
! Mathematical background of 2D CT
! 2D fan beam data acquisition
! Spiral CT from 2D towards 3D
! Recent technical developments and clinical images
! Fully 3D imaging
! 3D circular cone-beam CT
8
Single slice CT in sequence mode
collimated
X-ray source
In sequence mode the
moving X-ray source
and detector define an
image plane
x
y
→ 2D problem
detector with one row
4
9
2D Radon transform ℜ
The analytical approach of
reconstruction by projections has to
be done in the context of the Radon
transform ℜ
r
r r
r
ℜµ ( ρ , θ ) = ∫ d 2 r δ ( r ⋅ θ − ρ ) ⋅ µ ( r ) =
+∞
r
r
∫ dl µ ( ρ ⋅θ + l ⋅θ
⊥
y
line integral
normal vector
r
θ
)
−∞
Thus in the 2D case the Radon
transform ℜµ is identical to the
projection data p
r
θ⊥
distance ρ
r
p ( ρ , θ ) = ℜµ ( ρ , θ )
x
θ
r
 cos θ 

 sin θ 
θ =
with projection angle θ.
10
Sinogram
θ
The representation of the
projection data p ( ρ , θ ) r
(Radon transform ℜµ ( ρ , θ ))
in a ρ-θ-diagram is called
sinogram.
A point in spatial domain
appears as a sinusoidal curve
in the sinogram.
ρ
5
11
2D Radon data of a parallel projection
Radon data are represented by a
point in Radon space by the
correspondence of the position
vector:
r
! direction → normal vector θ
! length
→ distance ρ
array of parallel
x-ray beams
y
r
θ
An array of parallel x-ray beams
with projection angle θ samples
r
Radon data along the axis θ
perpendicular to the direction of
the x-ray beams hitting the origin
of the coordinate system.
x
Thus parallel projections of an
angular range of π (180°) would
cover complete object information.
corresponding
Radon data
12
Fourier- or central slice theorem in 2D
r
r
Fρ ℜµ ( ρ ,θ ) = ( F2 µ )(ω ρ ⋅θ )
The radial
1D Fourier transform Fρ of the Radon transform ℜµ
r
along θr is equal to the 2D Fourier transform F2 of the object µ
along θ perpendicular to the direction of the projection.
y
r
θ
array of parallel
x-ray beams
ωy
r
θ
ωx
x
radial Fourier
transform
Radon space
Fourier domain
6
13
Relationship between spatial-, Fourier- and
Radon-domain
r
µ (r )
spatial domain
2D Radon
transform
2D Fourier
transform
radial
1D Fourier
transform
r
ℜµ (ρ ,θ )
Radon domain
(F2 µ )(ωr ) = (F2 µ )(ω ρ , ωθ )
Fourier domain
14
Direct Fourier methods
! sample projection data p(ρ,θ) in an angular range θ ∈ [θ 0 , θ 0 + π ]
r
! 1D Fourier transform of each projection Fρ p ( ρ , θ ) = Fρ ℜµ ( ρ , θ )
⇒ yields (F2 µ )(ω ρ , ωθ ) 2D Fourier transform of object
distribution µ on a polar grid
! 2D Fourier inverse transformation
µ ( x, y ) =
θ 0 +π
∫
θ0
dωθ
ωy
+∞
∫ dω ρ
−∞
( F2 µ )(ω ρ , ωθ ) ⋅ ω ρ ⋅ e
i 2πω ρ ( x cos ωθ + y sin ωθ )
ramp filter due to polar coordinate system
ωx
Fourier domain
7
15
Direct Fourier methods using FFT
2D Fourier inverse transform
F2−1 ( F2 µ )(ω x , ω y ) = µ ( x, y)
by Fast Fourier Transforms (FFT)
ωy
ωy
ωx
ωx
resampling onto
a Cartesian grid
by interpolation
(numerically sensitive)
polar grid
Cartesian grid
16
Inverse Radon transform in 2D
r
1
r
µ ( r ) = − 2 ∫ dθ
4π
=
r
r
r 1 
ℜµ ( ρ , θ )
1
∫ dρ (rr ⋅θr − ρ )2 = − 4π 2 ∫ dθ  ℜµ ( ρ ,θ ) ∗ ρ 2  ρ =rr⋅θr
r
1 r −1
dθ Fρ ω ρ Fρ ℜµ ( ρ ,θ )
∫
2
backprojection
r r
ρ = r ⋅θ
ramp filtering
in Fourier domain
ω ρ = sign ω ρ ⋅ ω ρ
Hilbert trafo
convolution with
distribution kernel
in spatial domain
projection data p(ρ,θ)
derivative
Note, that due to the non-local behavior of the ramp filter in spatial
domain the projection data must not be truncated in ρ-direction.
8
17
Filtered backprojection (FBP)
For each projection do:
! apply a ramp-like filter
reconstruction
(image) plane
(either in spatial domain as a
convolution or in Fourier
domain as a multiplication)
! backproject filtered
projection data
projection
p(ρ,θ)
(accumulate contributions
of all projections)
Image quality can be
adjusted with the filter
kernel.
smearing back the
filtered projection data
along projection line
filtered
projection
data
~
p ( ρ ,θ )
18
Ram-Lak kernel
(Ramachandran & Lakshminarayanan, 1971)
discrete in spatial domain
continuous in Fourier domain
from Morneburg 1995
~
~
H (ω ρ ) = Fρ h ( ρ )
ω ρ ,ny
Characteristics of image results:
! sharp edges
! sensitive to noise
ωρ
 1 ωρ 
~

H (ωρ ) = ωρ ⋅ rect ⋅
 2 ω ρ ,ny 


9
19
Shepp-Logan kernel
(Shepp & Logan, 1974)
continuous in Fourier domain
~
~
H (ω ρ ) = Fρ h ( ρ )
from Morneburg 1995
discrete in spatial domain
ω ρ ,ny
Characteristics of image results:
! smoothed edges
! more robust to noise
ωρ

 1 ωρ 
ω 
~
 ⋅ sinc π ⋅ ρ 
H (ωρ ) = ωρ ⋅ rect ⋅
 2 ω ρ ,ny 
 2 ω ρ , ny 




20
! Introduction
! Mathematical background of 2D CT
! 2D fan beam data acquisition
! Spiral CT from 2D towards 3D
! Recent technical developments and clinical images
! Fully 3D imaging
! 3D circular cone-beam CT
10
21
Data acquisition in fan beam geometry
collimated
collimated
X-raysource
source
X-ray
Commercial scanner
of the third generation
acquire data in a
fan beam geometry.
detector with one row
detector with one row
22
2D fan beam geometry
Coordinates in parallel beam geometry:
θ
ρ
normal vector of particular line
distance to origin of coordinate system
x-ray focus
y
Coordinates in fan beam geometry:
φ
β
angle of x-ray source position
fan angle of particular line
normal θr
1
vectors r
θ2
β
φ
fan
angle
projection angle
Coordinate transformation:
π
p(θ , ρ ) → p fan (φ , β )
distance ρ
ce
ntr
a
l ra
y
+β
2
r
ρ = − rfocus ⋅ sin β
θ =φ +
x
11
23
Reconstruction methods for fan beam geometry
! Rebinning
! Resampling of fan beam to parallel beam
(requires additional interpolations)
! Application of reconstruction for parallel beam
(requires waiting time for acquisition of many projections)
! Reformulation of the inverse Radon transform
by a coordinate transformation from parallel to fan beam geometry
! Direct inversion
24
Rebinning of fan beam to parallel beam
To synthesize a parallel
projection of angle θ find all rays
such that
θ =φ +
π
+ β = const.
+3
+3
+2 +1
+1
+2
y
2
For this projections are needed
of the angular range
φ ∈ [θ − β max ,θ + β max ]
0
-1
-2
-1
-3
-2
-3
x
With βmax as maximum fan angle
β max = arcsin
focus
R FOV
R focus
βmax
Rfocus
RFOV
field-of-view
(FOV)
12
25
Reformulation of the inverse Radon transform
r
µ (r ) = −
r
µ (r ) = −
r 1
1
4π
2
∫ dθ  ρ
2
r 
∗ ℜµ ( ρ , θ ) 
 ρ = rr⋅θr
original formula
R
1
 1

dφ r r focus 2 ⋅  2 ∗ (cos β ⋅ p fan (φ , β ) )
4π 2 ∫
sin
β

r − r focus (φ ) 
r
r r
β = β ( r ), such that ρ = r ⋅θ
1/R2-weighting
in backprojection
→ increase of
computational expense
cos-weighting of
projection data
convolution equivalent
to ramp filtering
26
Convolution Kernels
Sharp
Spatial
Resolution
ULTRA
HIGH
B60f
ramp
HIGH
STANDARD
Smooth
B20f
SOFT
Noise
SOFT DETAIL
Low
High
Classification scheme.
Tradeoff:
spatial resolution ↔ noise
Fourier transform of some exemplary
convolution kernels for body scans (B)
in ultrafast mode (f)
13
27
Convolution kernel B20f (soft)
C=-700, W=800
C=10, W=200
The soft kernel B20f is appropriate for soft tissue imaging with a
good contrast resolution. For displaying the lung parenchyma the
image is too smooth.
28
Convolution kernel B60f (high)
C=-700, W=800
C=10, W=200
The sharp kernel B60f is appropriate for lung imaging with a good
spatial resolution. For displaying the soft tissue the image is too
noisy.
14
29
2D Radon data of a fan beam projection
A particular x-ray focus position
acquires Radon data on a circle in
Radon space.
The circle is characterized by
! diameter R focus
! x-ray position and origin are lying
on circle line
y
x
.
For R focus → ∞ the fan beam
geometry converges into the parallel
case.
Radon
data
x-ray focus
30
Sufficiency condition in fan beam geometry
Fan beam projections of an
angular range of π (180°)
do not cover complete
object information.
The angular range has to be
extended to
π + 2 ⋅ β max
Care has to be taken
of data redundancies,
since some but not all
Radon data are acquired
twice (unless angular range
equal 2π).
y
missing data
2βmax
x
field-of-view
(FOV)
15
31
Correction of data redundancies by
Parker weighting (Parker 1982)
φ
Although the degree of
redundancies is a discontinuous
step function, correction has to be
done by a smooth weighting
data
function.
π+2βmax
π
redundancies
E.g. Parker’s weight for the lower
triangular region
π
φ
w(φ , β ) = sin 2 ⋅
2 β max − β
for 0 ≤ φ ≤ 2( β max − β )
and similar expression for the
upper one.
2βmax
β
(φ,β)-representation
32
Local sufficiency condition (super short-scan)
An object point r can be
reconstructed exactly if it
sees a scan path segment
of angular range π. Thus,
an ROI can be
reconstructed without
acquiring complete data
of the object (super shortscan).
Specific algorithms are
needed for reconstruction
from a super short-scan
" F. Noo et al., BMP 2002
" H. Kudo et al., IEEE NSS
2002
y
object
x
point r
π
PI-line
scan path
segment
sufficient for
reconstruction
of point r
16
33
Examples of super short-scan trajectories and
associated region-of-interests
from F. Noo, M. Defrise,
R. Clackdoyle, and H. Kudo,
“Image reconstruction from
fan-beam projections on less
than a short scan”,
Physics in Medicine and
Biology 47 (2002) 2525-2546
34
How an algorithm builds up a reconstructed
image
" Contours are recovered
relatively early.
" Artifacts of low spatial
frequencies which
significantly disturb
contrast resolution are
removed just at the end
when data acquisition is
complete.
17
35
! Introduction
! Mathematical background of 2D CT
! 2D fan beam data acquisition
! Spiral CT from 2D towards 3D
! Recent technical developments
and clinical images
! Fully 3D imaging
! 3D circular cone-beam CT
36
Single slice CT in spiral mode
In the patient
coordinate system the
x-ray source and the
detector move on a
spiral.
collimated
X-ray source
z
x
In spiral mode the
moving X-ray source
and detector do not
define an image plane
any more.
→ 3D problem
detector
with one row
patient
coordinate
y system
continuous
table
movement
18
37
Reduction to a 2D reconstruction problem
In a single row scanner there are
always projection data at zpositions z(φ) close to the image
plane at zimage.
Therefore 2D projection data
p2D(φ,β) can be synthesized by
interpolation between spiral data
pspiral of equivalent projection angle
which are acquired on opposite
sides of the image plane
p 2 D (φ , β ) =
z
w ⋅ p spiral (φ ′, β ) + (1 − w) ⋅ p spiral (φ ′ + 2π , β )
(
for a given projection angle nearest
x-ray focus position on opposite
side of the image plane
)
with weight w ≡ w z (φ ′) − z focus ,
φ = mod 2π φ ′ and
z (φ ′) − z image ≤ pitch ⋅ N ⋅ ∆z
38
Benefits of spiral CT
" Fast scanning of large
anatomical volumes
" Gapless data
acquisition during one
breathhold
" no missing lesions
" increase of zresolution in MPR’s
by overlapping
reconstruction
from Kalender 2000
" Retrospective
reconstruction with
arbitrary slice
increments
19
39
Multi slice CT
The increased number of
detector rows can be used for
larger
volume
collimated
X-ray source
z
x
shorter
scan time
improved
z-resolution
patient
coordinate
y system
continuous
table
movement
With increasing cone angle more and
more sophisticated reconstruction
algorithms are required to provide
good image quality.
further increase of the
number of detector rows
40
“Moore’s Law” for CT?
Will the race for more slices go on?
So far: doubling every 2.5 years
Sensation 64
Adaptive Multiple Plane
Reconstruction (AMPR)
Schaller, Flohr et al 2000
Adaptive Axial Interpolation
Schaller, Flohr et al 1998
20
41
Advanced Single Slice Rebinning Algorithm
(ASSR)
The image plane is tilted to minimize the mean z-distance of the
image plane to the x-ray source positions contributing to a shortscan. Thus 2D projection data for the tilted image plane can be
synthesized properly. After 2D reconstruction of a bunch of image
planes with different tilt angles ordinary axial slices are achieved
by reformatting.
z-axis
z-axis
contributing
source positions
plane
tilted image
12 detector rows,
pitch 1.5 (18)
projection of scan geometry
42
“Moore’s Law” for CT?
Will the race for more slices go on?
3D Backprojection with
Opt. Filter + Weighting (R3D-FBP)
Stierstorfer, Bruder, Rauscher
et al 2002
Segmented Multiple Plane
Reconstruction (SMPR)
Stierstorfer, Bruder et al 2001
Sensation 64
Adaptive Multiple Plane
Reconstruction (AMPR)
Schaller, Flohr et al 2000
Adaptive Axial Interpolation
Schaller, Flohr et al 1998
21
43
First steps to fully 3D:
3D Filtered Backprojection (R3D-FBP)
z
! So far all reconstruction
algorithms were a reduction of
the 3D problem to a 2D one.
! Simple, approximate 3D
solution:
slice
profile
filter
direction
! filter detector image in the
direction of the spiral tangent
! 3D backprojection
! weighted and normalized
accumulation according to a
user defined slice profile
tangent
44
Image quality of the R3D-FBP algorithm
Clock phantom
64-row detector of 1mm collimation, pitch 1.0 (64), axial images
SMPR
R3D-FBP
exact
Due to the approximations in filtering and data accumulation
some artifacts remain in R3D-FBP. The ultima ratio is an exact
3D algorithm.
22
45
What is the clinical benefit of ultra-fast spiral
scanning?
Scan time of the entire thorax (350mm)
at a 0.75mm collimation
100 sec
breath hold time
10 sec
Single
slice
16
slice
128
slice
Beyond the threshold of the breath hold time there is no huge
clinical benefit foreseen for further reducing the scan time.
46
Focus on increased isotropic spatial resolution
with Siemens’ scanner SOMATOM Sensation 64
Double z-sampling
0.6
0,6 mm 0,6 mm
Oversampling
Z
! 64 slices per rotation
! Routine 0.4 mm
! 64-slice high speed data
isotropic resolution,
with no increase in
dose
32 x 0.6 mm
64 Channel
Electronics
32 Slice Detector
3264
Slice
Detection
Slice
DAS
acquisition electronics
with 2.5 Gbit/s
(>500 DVD players in
parallel)
23
47
Headline
SOMATOM
Sensation 64
33 sec for 1570 mm
64 x 0.6mm
Resolution 0.4 mm
Rotation 0.5sec
120 kV / 148mAs
Courtesy of University of Erlangen and University of Tübingen
48
SOMATOM
Sensation 64
10sec for 165mm
64 x 0.6mm (2x32)
Resolution 0.4 mm
Rotation 1 sec
120 kV / 450mAs
Courtesy of University of Erlangen, Department of Radiology and Institute of Medical Physisc
24
49
SOMATOM
Sensation 64
22sec for 260mm
64 x 0.6mm (2x32)
Resolution 0.4mm
Rotation 0.33 sec
120 kV / 760mAs
Heart rate 95bpm
Courtesy of University Medical Center Grosshadern, Munich, Institute of Clinical Radiology
50
Headline
SOMATOM
Sensation 64
22sec for 260mm
64 x 0.6mm (2x32)
Resolution 0.4mm
Rotation 0.33 sec
120 kV / 760mAs
Heart rate 95bpm
Courtesy of University Medical Center Grosshadern, Munich, Institute of Clinical Radiology
25
51
SOMATOM
Sensation 64
11sec for 144 mm
64 x 0.6mm (2x32)
Resolution 0.4 mm
Rotation 0.37 sec
120 kV / 500 mAs
Courtesy of University of Erlangen, Departments of Radiology and Cardiology DHZ Munich
52
Headline
Calcified Lesion with
soft plaque
SOMATOM
Sensation 64
11sec for 144 mm
64 x 0.6mm (2x32)
Resolution 0.4 mm
Rotation 0.37 sec
120 kV / 500 mAs
3mm Stent
Courtesy of University of Erlangen, Department of Radiology and Cardiology DHZ Munich
26
53
SOMATOM
Sensation 64
11 sec for 640 mm
64 x 0.6mm
Resolution 0.4 mm
Rotation 0.37 sec
120 kV / 150 mAs
Courtesy of University of Erlangen and University of Tübingen
54
SOMATOM
Sensation 64
SOMATOM
Sensation 64
12 sec for 610 mm
64 x 0.6mm
Resolution 0.4 mm
Rotation 0.5 sec
120 kV / 150 mAs
Conventional
Angio
Courtesy of University of Erlangen, Department of Radiology and Institute of Medical Physics
27
55
SOMATOM
Sensation 64
11sec for 255mm
64 x 0.6mm (2x32)
Resolution 0.4 mm
Rotation 0.5 sec
120 kV / 90mAs
Pediatric Patient
Courtesy of University of Erlangen, Department of Radiology and Institute of Medical Physisc
56
! Introduction
! Mathematical background of 2D CT
! 2D fan beam data acquisition
! Spiral CT from 2D towards 3D
! Recent technical developments and clinical images
! Fully 3D imaging
! 3D circular cone-beam CT
28
57
Fully 3D imaging in the “far” future
The trend of increasing the
number of detector rows might
end in the use of a large area
detector.
For such a scanning device the
approximation of a reduction to
a 2D reconstruction problem
(ASSR, AMPR, SMPR) will not
hold any more. Even
approximate methods like the
R3D-FBP might be critical.
Algorithms will be required fully
considering the 3D scanning
geometry.
collimated
X-ray source
z
x
patient
coordinate
system
y
continuous
table
movement
use of an area detector
covering large volumes
58
n-dimensional Radon transform ℜ
r
r r
r
ℜµ ( ρ , θ ) = ∫ d n r δ ( r ⋅ θ − ρ ) ⋅ µ ( r )
2D
integration along a line
3D
...
integration on a plane
...
nD
integration on a (n-1)-dimensional hyper plane
29
59
3D Radon data in cone-beam geometry
rce
det
ect
integration planes
for generating
Radon data
or
ys
ou
z
con
eo
pa
th
f x-
of
x
ray
s
- ra
y
x
object
x-ray source
planes are sampled by fan-beams
→ only radial derivative
of Radon data can be
acquired (Grangeat 1991)
→ sufficient for reconstruction
60
Inverse Radon transform in 3D
r
µ (r ) = −
1
8π 2
r
∫ dθ
backprojection
r
∂2
ℜµ ( ρ ,θ )
2
r r
∂ρ
ρ = r ⋅θ
plane integral of object
Unlike the 2D case the inversion acts locally
in the 3D Radon space.
30
61
Beginning of a completely novel analysis
! Fourier or central slice theorem in 3D
! Sufficiency conditions
! Tuy condition
! Concept of PI-lines
! Long object problem (axial truncation)
! Data redundancies
! Redundancies are obvious only when collecting 3D Radon data
! Efficient reconstruction algorithms
! Find FBP-type algorithms with spatially invariant 1D filtering
! ....
62
Alexander Katsevich’s exact reconstruction
algorithm for cone beam spiral CT
C=50HU
W=420HU
Reference image, reconstructed
from SOMATOM Sensation 16 data
Reconstruction from synthesized
projection data with a virtual detector
of 284 rows, pitch 1.35 (384)
table feed per turn 192mm
→ 576mm/s (2.1km/h)
31
63
! Introduction
! Mathematical background of 2D CT
! 2D fan beam data acquisition
! Spiral CT from 2D towards 3D
! Recent technical developments and clinical images
! Fully 3D imaging
! 3D circular cone-beam CT
64
Back to sequential scanning:
Circular cone-beam CT
collimated
X-ray source
A complete ROI can be
scanned in a single rotation
with a large area detector
system.
z
The method of choice for
circular cone-beam is the
robust and efficient
Feldkamp algorithm.
However, one has to be
aware that a circular scan
does not provide a
complete data set in cone
beam geometry.
x
patient
coordinate
y system
continuous
table
movement
32
65
Feldkamp algorithm
r
µ (r ) =
horizontal
1D filtering
2π
R focus ⋅ R focus − detector
1
dλ r r
∫
r r 2 ⋅ hramp (u ) ∗ (cos ϑ ⋅ pcone (λ ; u , v )) u ,v as projection of rr
2 0
r − r focus ⋅ (eu × ev )
(
data redundancy
for full circle
distance weighting
(
)
row-by-row 1D filtering in
horizontal direction with
conventional ramp filter
cosine weighting:
R focus − detector
cos ϑ =
2
R focus − detector + u 2 + v 2
)
Properties of the Feldkamp algorithm:
" Image in mid-plane is exact (identical to fan beam case).
" Average along z direction is exact.
" Volume reconstruction is exact for objects homogenous in z.
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Incomplete data sampling in pure circular
scanning → cone artifacts
z
missing data
y
x
Thorax simulation study.
Coronal slice. C=0, W=200
3D Radon space for a circular scan
Due to incomplete data sampling cone artifacts show up at sharp
z-edges of objects with high contrast. These artifacts can be
avoided by variations of the scan path only: e.g. circle+line, 2
tilted circles, sinusoidal (saddle), spiral, etc.
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Dynamic volume imaging.
Technique of the future?
Applications foreseen
! Phase restricted CTA /
dynamic vascular imaging
!
Heart, brain and kidney
continuously
rotating
source-detector
assembly
! Volume Perfusion
Heart, brain and kidney
! Partially liver and lung
!
tube
! 3D Intervention
!
Biopsy needle guidance
!
Augmented reality
detector
prototype study, slow rotation speed, flat panel detector
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3D reconstruction for
interventional orthopedics /
surgery
Inexpensive, easily
accessible imaging device
in the operating room with a
mobile C-arm system.
Reconstructed slice images for
control of the placement of screws
etc. in osteosynthesis. Today,
imaging of high contrast objects
only.
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3D reconstruction for interventional angiography
Data acquisition
directly in the
intervention room
before, during, or after
treatment with a
conventionally used
angiographic device.
Set of 2D projection
data at a circular short
scan trajectory with
intra arterial contrast
agent (inconsistent
data!).
3D reconstruction of a
carotis segment with a
stent.
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Superior spatial resolution
of C-arm based imaging
Due to the small pixel
size of the radiographic
and fluoroscopic flat
panel detectors used
(approx. 180µm) a better
spatial resolution is
achieved compared to
conventional computed
tomography.
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C-arm based imaging towards low contrast
Image quality of new
C-arm devices might be
improved towards low
contrast resolution by
" replacement of image
intensifier by flat panel
detectors
" increased bit depth of
the detector
" increased number of
projections
" corrections of scatter,
beam hardening,
ringing, etc.
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Courtesy of Dr. Loose, Klinikum Nürnberg-Nord
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