Iterative reconstruction for metal
artifact reduction in CT
• the problem
• projection completion
• polychromatic ML model for CT
• local models, bowtie,…
• examples
Katrien Van Slambrouck, Johan Nuyts
Nuclear Medicine, KU Leuven
1
the problem
CT
iron
y
y(s, )  b(s, )e
yi  bi e
 
   ( x ) dx
L
  j lij j
ln(b/y)
2
the problem
Double knee prosthesis
Double hip prosthesis
Dental fillings
Cause of metal artifacts:
• Beam hardening
• Nonlinear partial volume effects
• Noise
• Scatter
• resolution (crosstalk, afterglow)
• (Motion)
Mouse bone and titanium
screw (microCT)
3
Artifacts in CT
Beam hardening
Energy (keV)
10 cm
water
Normalized intensity (%)
10 cm
water
Normalized intensity (%)
Polychromatic spectrum, beam hardens when going through the object
Low energy photons are more likely absorbed
Normalized intensity (%)
I.
Energy (keV)
Energy (keV)
Typical artifact appearance: dark streaks in between metals, dark shades
around metals (and cupping)
Iron in water
Amalgam in PMMA
Artifacts in CT
II. (Non)-linear partial volume effects
•
•
Linear: voxels only partly filled with particular substance
Non-linear: averaging over beam width, focal spot, …
I0
µ2
µ1
I
Typical artifact appearance: dark and white streaks connecting edges
Iron in water
Amalgam in PMMA
Artifacts in CT
III. Scatter
•
•
Compton scatter: deviation form original trajectory
Scatter grids?
I0
Typical artifact appearance: dark streaks in between metals, dark shades
around metals (and cupping)
Iron in water
Amalgam in PMMA
Artifacts in CT
IV. Noise
•
Quantum nature: ± Poisson distribution
Typical artifact appearance: streaks around and in between metals
Iron in water
Amalgam in PMMA
projection completion

Initial FBP reconstruction

Segment the metals and project

Remove metal projections for sinogram

Interpolate (e.g. linear, polynomial, …)

Reconstruct (FBP) and paste metal parts
• Kalender W. et aI. "Reduction of CT artifacts caused by metallic impants." Radiology, 1987
• Glover G. and Pelc N. "An algorithm for the reduction of metal clip artifacts in CT reconstructions." Med. Phys., 1981
• Mahnken A. et al, "A new algoritbm for metal artifact reduction in computed tomogrpaby, In vitro and in vivo evaluation after
total hip replacement." Investigative Radiology, 2003
8
projection completion
window 600 HU
H 2O
PMMA
Fe
9
projection completion
window 600 HU
true object
FBP
projection completion
10
projection completion
1
2
zeroed metal trace
linear interpolation
• Muller I., Buzug T.M., "Spurious structures created by interpolation-based Ct metal artifact reduction." Proc. of SPIE, 2009
• Meyer E. et al, "Normalized metal artifact reduction (NMAR) in computed tomography." Med. Phys., 2010
11
NMAR
window 600 HU
sinogram
interpolated
sinogram of
segmentation
normalized
sinogram
• Muller I., Buzug T.M., "Spurious structures created by interpolation-based Ct metal artifact reduction." Proc. of SPIE, 2009
• Meyer E. et al, "Normalized metal artifact reduction (NMAR) in computed tomography." Med. Phys., 2010
12
NMAR
1
2
sinogram,
metals erased
sinogram of
the segmented
reconstruction
13
NMAR
1
2
normalized
sinogram,
metals erased
interpolated
sinogram
14
NMAR
unnormalized
interpolated
sinogram
15
proj.completion and NMAR
window 300 HU
true object
FBP
projection
completion
NMAR
16
Maximum Likelihood for CT
CT
y(s, )  b(s, )e
yi  bi e
 
   ( x ) dx
L
  j lij j
17
Maximum Likelihood for CT
CT
data
yi  bi e
recon
  j lij j
18
Maximum Likelihood for CT
one wishes to find recon that
maximizes p(recon | data)
data
recon
computing p(recon | data)
difficult inverse problem
computing p(data | recon)
“easy” forward problem
Bayes:
p(data | recon) p(recon)
p(recon | data) =
~
p(data)
MAP
ML
19
Maximum Likelihood for CT
p(recon | data) ~
p(data | recon)
data
recon
projection
j
j = 1..J
Poisson
p(data | recon)
yˆ i  bi exp   j  jlij 


  p( yi | yˆ i )
i
y
 yˆ i yˆ i i
 e
y i!
i
i = 1..I
ln(p(data | recon)) =~ L(data | recon) =
 yi ln yˆ i  yˆ i  ln( yi! )
i
20
Maximum Likelihood for CT
L(data | recon)
  yi ln yi  yi 
yi  b i e
  j  jlij
i
iterative maximisation of L:
 j 
 j ilij y i  y i 
l y  l
i ij i
k ik
j  0
k
21
 j 
 j ilij y i  y i 
l y  l
i ij i
k ik
k
MLTR
convex algorithm [1]
patchwork: local update [2,3]
[1] Lange, Fessler, “Globally convergent algorithms for maximum a posteriori transmission
tomography”, IEEE Trans Image Proc, 1995
[2] JA Fessler et al, "Grouped-coordinate ascent algorithm for penalized likelihood transmission
image reconstruction." IEEE Trans Med Imaging 1997.
[3] Fessler, Donghwan, "Axial block coordinate descent (ABCD) algorithm for X-ray CT image
reconstruction.“ Fully 3D 2011
22
MLTR
MEASUREMENT
COMPARE
UPDATE
RECON
REPROJECTION
23
MLTR
validation
Siemens Sensation 16
Siemens
MLTR
24
models for iterative reconstruction
I
Poisson Likelihood:
L   yi ln yˆ i  yˆ i 
i
yi
yˆ i
bi
measured data
data computed from current
reconstruction image
Projection model:
• monochromatic:
 J


yˆ i  bi exp   lij j 
 j



yi
25
models for iterative reconstruction
I
Poisson Likelihood:
L   yi ln yˆ i  yˆ i  intensity b
ik
i
yi
yˆ i
measured data
data computed from current
reconstruction image
Projection model:
• monochromatic:
• 1 material
polychromatic:
MLTR_C
“water correction”
 J


yˆ i  bi exp   lij j 
 j





J

yˆ i   bik exp  Pk  lij j 


k
j


energy
energy k
Pk 
kwater
water
ref
26
models for iterative reconstruction
I
Poisson Likelihood:
L   yi ln yˆ i  yˆ i  intensity b
ik
i
Projection model:
•
energy k
Full Polychromatic Model – IMPACT
 J


yˆ i  bi exp   lij j 
 j



 J


yˆ i   bik exp   lij jk 
 j

k


K
27
models for iterative reconstruction
•
Full Polychromatic Model – IMPACT
 J


yˆ i  bi exp   lij j 
 j



 J


yˆ i   bik exp   lij jk 
 j

k


K
al
water
attenuation
Compton
photo-electric
jk = photo-electric + Compton at energy k
jk =
fj ∙ photok + j ∙ Comptonk
Comptonk = Klein-Nishina (energy)
Photok
≈ 1 / energy3
28
models for iterative reconstruction
•
Full Polychromatic Model – IMPACT
 J


yˆ i  bi exp   lij j 
 j



 J


yˆ i   bik exp   lij jk 
 j

k


K
F and  (1/cm)
f
jk =
fj ∙ photok + j ∙ Comptonk

jk = fj∙ photok + j ∙ Comptonk
mono (1/cm)
29
models for iterative reconstruction
F and  (1/cm)
f

mono (1/cm)
30
patches, local models
 j 
 j ilij y i  y i 
l y  l
i ij i
k ik
k
MLTR
convex algorithm [1]
patchwork: local update [2,3]
[1] Lange, Fessler, “Globally convergent algorithms for maximum a posteriori transmission
tomography”, IEEE Trans Image Proc, 1995
[2] JA Fessler et al, "Grouped-coordinate ascent algorithm for penalized likelihood transmission
image reconstruction." IEEE Trans Med Imaging 1997.
[3] Fessler, Donghwan, "Axial block coordinate descent (ABCD) algorithm for X-ray CT image
reconstruction.“ Fully 3D 2011
31
bowtie, BHC
intensity bik
e-
energy k
• raw CT data not corrected for beam hardening
• send spectrum through filter and bowtie
bik = spectrum(k) x bowtie(i)
32
patches, local models
IMPACT is complex and slow,
MLTR and MLTR_C are simpler and faster
PATCH 3
Find the metals
Define patches
IMPACT in metals
MLTR_C elsewhere
PATCH 2
PATCH 4
PATCH 1
33
clinical CT (Siemens Sensation 16)
Body shaped phantom
34
sequential CT (Siemens Sensation 16)
Body shaped phantom
FBP
Regular PC
PC NMAR
IMPACT
IMPACT PATCH
MLTR_C + IMPACT
20 iter x 116 subsets
35
sequential CT (Siemens Sensation 16)
Body shaped phantom
Ti Al V
CoCr..
water
aluminum
PMMA
water
Black = FBP
Blue = PC-NMAR
Red = IMPACT PATCH
36
helical CT
sequential 2 x 1mm
helical 16 x 0.75mm
37
helical CT
MIP
metal patches,
uniform init.
FBP
IMPACT
no patches,
NMAR init.
NMAR
metal patches,
NMAR init.
5 iter x 116 subsets
38
helical CT
MIP
metal patches,
uniform init.
FBP
IMPACT
no patches,
NMAR init.
NMAR
metal patches,
NMAR init.
39
helical CT
FBP
NMAR
IMPACT
10
5 it
40
helical CT
We give patches same x-y sampling but increased z-sampling:
impact, regular z
z-sampling x 3
41
to do
• after 5..10 x 100 iterations with patches still incomplete convergence
• persistent artifacts near flat edges of metal implants
• we currently think it is not
o scatter
o non-linear partial volume effect
o crosstalk, afterglow
o detector dead space
42
better physical model
better reconstruction
Katrien Van Slambrouck
Bruno De Man
Karl Stierstorfer,
David Faul, Siemens
thanks
43