Karl Stierstorfer, Rainer Raupach, Thomas Flohr, Siemens Healthcare
Iterative Reconstruction in CT –
the Siemens Approach
© Siemens AG 2015 All rights reserved.
Answers for life.
Standard CT Reconstruction:
Filtered Backprojection (FBP)
raw data domain
CT raw data
image domain
FBP
CT image
reconstruction
© Siemens AG 2015 All rights reserved.
K. Stierstorfer, Siemens Healthcare
Page 2
Limitations of Filtered Backprojection (FBP)
 FBP is only an approximate realization
of the inverse Radon transformation
 „geometric artifacts“
(cone beam artifacts)
 FBP uses raw data with equal weight
irrespectively of their statistical quality
 streak artifacts
 Tradeoff between spatial resolution
and noise (linear algorithm)
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smooth
low noise
sharp
high noise
Handout 1
Iterative Reconstruction
Basic Idea: Introduction of a Correction Loop
raw data domain
image domain
correction
image
FBP
CT raw data +
reconstruction
+
forward
projection
CT
image
+
 Simulation of a CT scan from the images
 Modeling of system features (focus, detector, …)
 Validation of the reconstructed images w.r.t. the measured data
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K. Stierstorfer, Siemens Healthcare
axial
axial
Artifact Reduction by IR
coronal
coronal
sagittal
FBP
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Standard
I-FBP
2 iterations
I-FBP, 2 iterations
2014-09-17
R. Raupach / H IM CR R&D PA
Iterative Reconstruction with Statistical Optimization:
Statistical Weighting and Regularization
raw data domain
CT raw +
data
statistical
weighting
image domain
FBP
correction
image
-
forward
projection
 Weight data according
to their statistical quality,
typically  1 / variance
+
CT
image
-
regularization
(prior knowledge)
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K. Stierstorfer, Siemens Healthcare
Handout 2
Regularization / Prior Knowledge
Regularization
+
CT
image
 Local smoothness constraint – this is where prior
knowledge is introduced
-
 Ensures convergence of the iterative reconstruction
 Is the essential mechanism for noise and dose
reduction!
regularization
(prior knowledge)
 Has to be non-linear to get rid of the tradeoff
between resolution and noise
How it works
 Estimate/model the (local) image standard deviation
 Separate information and noise on the basis of statistical significance
 intelligent high-pass filter based on local contrast-to-noise
 Subtract the detected noise
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K. Stierstorfer, Siemens Healthcare
Advantages of Non-Linear Regularization
versus Linear Filtering
 = 53 HU
 = 21 HU
 = 21 HU
WFBP
IR, 5 iterations
WFBP, soft kernel (=WFBPsoft)
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Page 9
2014-09-17
(81,167): -110.464
(67,169): 3
Diff (IR – WFBP)
Diff (WFBP
R. Raupach
/ HWFBP)
IM CR R&D PA
soft –
General Approach
For the different objectives of iterative reconstruction, choose the domain
most efficient to accomplish them:
Need low signal data enhancement?
 work in the raw data domain; apply statistical modeling
Need (cone beam) artifact reduction?
 need a full raw data/image loop including a forward projection
of images
Need noise reduction?
 best apply iterative regularization in image domain
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K. Stierstorfer, Siemens Healthcare
Handout 3
Iteration Scheme
best image
Maximum Likelihood:
data
image
f  arg max P( pmeas | f )
f
“The best image is the most likely image based on the data”
Additional assumption: Data are nearly Gaussian
0.14
Poisson
Gauss
0.12
 Problem reduces to a minimization problem
(Penalized weighted least squares):
0.1
There is virtually no
difference between
Poisson and Gauss,
even for as few as
10 photons…
0.08
0.06
best image
data weight
proj. operator
regularizer
2
1

f  arg min W  ( pmeas  Pf )  R( f ) 
f
2

0.04
0.02
0
0
5
10
15
20
25
30
35
40
45
50
Iterative solution e.g. by steepest descent:
reconstruction
(backprojection)
f n  f n 1    QW  pmeas  Pf n 1   R f n 1 
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K. Stierstorfer, Siemens Healthcare
Iteration Scheme
Now we have:
f n  f n 1    QW  pmeas  Pf n 1   Rf n 1 
correction image
Define …
regularization
X W  QWP
1. … the operator
 Performs forward projection, then weighting, followed by reconstruction, i.e.
takes an image and returns an image
 XW depends on the raw data via W, but can be pre-calculated
2. … a „weighted“ image
fW  QWpmeas
fW  QWpmeas
Qpmeas
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K. Stierstorfer, Siemens Healthcare
Page 12
Iteration Scheme
f n  f n 1    QW  pmeas  Pf n 1   Rf n 1 
correction image
regularization

X W  QWP
fW  QWpmeas
f n    fW  1    X W  R  f n 1
 No access to measured raw data necessary in the loop!
 Iterative image manipulation can be equivalent to a noise weighted
raw data loop
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K. Stierstorfer, Siemens Healthcare
Handout 4
General Approach
Is system modeling essential for noise reduction?
 No – noise reduction is achieved exclusively through the
regularization term
Does system modeling improve the resolution?
 No – for a stable reconstruction, the resolution is still limited by the
focus size, the detector aperture and the data sampling
Is a raw data loop essential for noise reduction?
 No – cf. previous slides
(For a similar – and mathematically rigorous – approach, see also:
G. L. Zeng, Noise-weighted spatial domain FBP algorithm, Med. Phys. 41,
051906 (2014))
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2015-07
K. Stierstorfer, Siemens Healthcare
General Approach
Relevant questions for choosing an IR algorithm are:

How can the IR approach be implemented efficiently
with clinically valuable results and acceptable computational performance?

How can a natural noise texture be realized? (Radiologists reject “plasticlike” de-noised images)

What is the benefit with routine reconstruction parameters (e.g. thick
slices)?

How can we predict/assess the achievable dose reduction in a
meaningful way?
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K. Stierstorfer, Siemens Healthcare
Siemens Generations of IR:
IRIS – Iterative Reconstruction in Image Space
 No reduction of geometric (cone beam) artifacts
 Limited potential for anisotropic noise distribution (e.g. shoulder)
Master 3D
Volume
+/-
Statistical
Modeling
(Image)
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K. Stierstorfer, Siemens Healthcare
Handout 5
Siemens Generations of IR:
SAFIRE – Sinogram Affirmed Iterative Reconstruction
FBP
+/-
Master 3D
Volume
+/Loop B
Statistical
Modeling
(Image)
Loop A
System
Modeling
(FP)
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K. Stierstorfer, Siemens Healthcare
Siemens Generations of IR:
ADMIRE – Advanced Modeling Iterative Reconstruction
Improved performance
at very low signals
FBP
Statistical
Modeling
(Raw)
+/-
Master 3D
Volume
+/Loop B
Statistical
Modeling
(Image)
Loop A
System
Modeling
(FP)
• Improved performance
for thick slices
• Improved noise texture
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K. Stierstorfer, Siemens Healthcare
ADMIRE – Advanced Modeling Iterative Reconstruction
Standard
Br40
ADMIRE
Br40/5
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K. Stierstorfer, Siemens Healthcare
Handout 6
ADMIRE – Advanced Modeling Iterative Reconstruction
Standard
Bv40
ADMIRE
Bv40/5
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K. Stierstorfer, Siemens Healthcare
ADMIRE – Advanced Modeling Iterative Reconstruction
Standard
Hc44
ADMIRE
Hc44/5
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K. Stierstorfer, Siemens Healthcare
ADMIRE – Advanced Modeling Iterative Reconstruction
Low Dose
CTDIvol 0.23 mGy / DLP 8.3 mGycm / eff. Dose 0.12 mSv
Standard
Bl64
ADMIRE
Bl64/5
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K. Stierstorfer, Siemens Healthcare
Handout 7
ADMIRE – Advanced Modeling Iterative Reconstruction
Extremely Low Dose
CTDIvol: 0.04 mGy / DLP 1.64 mGycm / eff. Dose 0.025 mSv
Standard
Bl64
SAFIRE
Bl64/5
ADMIRE
Bl64/5
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K. Stierstorfer, Siemens Healthcare
What Should Be Compared?
up to 55% less noise
30% less noise
35% less noise
 = 17.6 HU
 = 12.3 HU
 = 7.8 HU
 = 26.8 HU
plain FBP
Siemens WFBP
reconstruction
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Page 24
2014-09-17
1st generation IR
slice 0.75 mm
W = 250
C = 40
2nd generation IR
R. Raupach / H IM CR R&D PA
Iterative Reconstruction
Evaluation with Model or Human Observers
How low can you go?
 IR leads to a noise level comparable with higher radiation dose, even at
about 90% dose reduction
 But: diagnostic equivalence not necessarily given - some details may be lost.
 Technical metrics (noise, contrast, …) are not sufficient (cf. previous talk)
 More sophisticated objective tests are required
Low Dose IR [2.3 mSv]
Full dose FBP [19 mSv]

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K. Stierstorfer, Siemens Healthcare
Handout 8
Iterative Reconstruction
Evaluation with Model Observers
 Definition of a meaningful task
 Usage of a „Channelized Hotelling Observer“
 mimics visual perception
positive
negative
Task: lesion present or not?
true positive findings
 ROC analysis
WFBP 120 mAs (100%)
WFBP 48 mAs (40%)
SAFIRE 48 mAs
false positive findings
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K. Stierstorfer, Siemens Healthcare
What is a relevant imaging task?
• Currently, all claims of dose reduction are based on studies with low
contrast detection tasks („Is there a lesion or not?“), possibly with
localization („Where is the lesion?“).
• But: Is this the most relevant task in CT?
There are other tasks like distinction of different shapes („Lesion
round or hexagon?“, „Lesion fuzzy or sharply delineated?“) which
might be closer to typical clinical applications of CT. However, they
are less easy to standardize – and it may be more difficult to build
phantoms!
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2015-07
K. Stierstorfer, Siemens Healthcare
Conclusion

Iterative reconstruction is a meaningful way to improve various aspects of CT
image quality.

Various flavors of iterative reconstruction are available: data domain, image
domain or data+image domain. They should be combined in a meaningful
way to achieve the desired objectives efficiently.

With respect to noise, IR is equivalent to a complex local, non-isotropic
adaptive filter realizing a spatial resolution depending on the local
contrast/noise ratio.

Important questions from a clinical perspective:


Image quality aspects: Natural noise texture? Edge appearance? Good
also for thicker slice widths?

What is the dose reduction potential for various tasks?

Is it capable of routine usage?
Dose reduction claims should be taken with a grain of salt: What is the point
of comparison in a relative claim? Is the task clinically relevant?
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K. Stierstorfer, Siemens Healthcare
Handout 9
Thank you!
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2015-07
K. Stierstorfer, Siemens Healthcare
Handout 10