Iterative reconstruction for metal artifact reduction in CT

1

• the problem

• projection completion

• polychromatic ML model for CT

• local models, bowtie,…

• examples

Katrien Van Slambrouck, Johan Nuyts

Nuclear Medicine, KU Leuven

the problem

2

y

CTCT

jj ijlii eby

L

xd)x(e),s(b),s(y

ln(b/y)

iron

the problem

Double hip prosthesisDouble knee 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)

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I. Beam hardeningPolychromatic spectrum, beam hardens when going through the objectLow energy photons are more likely absorbed

Artifacts in CT

Energy (keV)

10 cm water

10 cm water

Energy (keV) Energy (keV)

Nor

mal

ized

inte

nsity

(%)

Nor

mal

ized

inte

nsity

(%)

Nor

mal

ized

inte

nsity

(%)

Typical artifact appearance: dark streaks in between metals, dark shades around metals (and cupping)

Iron in water Amalgam in PMMA

II. (Non)-linear partial volume effects• Linear: voxels only partly filled with particular substance• Non-linear: averaging over beam width, focal spot, …

I0

I

µ1µ2

Artifacts in CT

Typical artifact appearance: dark and white streaks connecting edges

Iron in water Amalgam in PMMA

III. Scatter• Compton scatter: deviation form original trajectory • Scatter grids?

Artifacts in CT

I0

Iron in water Amalgam in PMMA

Typical artifact appearance: dark streaks in between metals, dark shades around metals (and cupping)

IV. Noise• Quantum nature: ± Poisson distribution

Artifacts in CT

Iron in water Amalgam in PMMA

Typical artifact appearance: streaks around and in between metals

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

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• 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

projection completion

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window 600 HU

Fe

PMMAH2O

projection completion

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true object FBP projection completion

window 600 HU

1

projection completion

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2

• 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

zeroed metal trace

linear interpolation

NMAR

12• 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

sinogram interpolated sinogram ofsegmentation

normalizedsinogram

window 600 HU

NMAR

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1

2

sinogram,metals erased

sinogram ofthe segmentedreconstruction

NMAR

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1

2

normalizedsinogram,metals erased

interpolatedsinogram

NMAR

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unnormalizedinterpolatedsinogram

proj.completion and NMAR

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true object FBP projectioncompletion

window 300 HU

NMAR

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CTCT

jj ijlii eby

Maximum Likelihood for CT

L

xd)x(e),s(b),s(y

Maximum Likelihood for CT

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CTCT

jj ijlii eby

data recon

computing p(recon | data) difficult inverse problem

computing p(data | recon) “easy” forward problem

one wishes to find recon that maximizes p(recon | data)

Bayes:

p(recon | data) = p(data | recon) p(recon)

p(data)

data recon

~

Maximum Likelihood for CT

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MAP

ML

Maximum Likelihood for CT

p(recon | data) ~

p(data | recon)

projection Poisson

j

j ijjii lexpby

j = 1..Ji = 1..I

i i

yiy!y

yei

i

i

ii )y|y(p

i

iiii )!yln(yylnyln(p(data | recon)) = L(data | recon) = ~

p(data | recon)recon data

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Maximum Likelihood for CT

i

iii yylnyL(data | recon) j ijjl

ii eby

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i k kikiij

i iiijjj lyl

yyl

iterative maximisation of L:

0j

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MLTR

convex algorithm [1]

[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

patchwork: local update [2,3]

i k kikiij

i iiijjj lyl

yyl

MLTR

MEASUREMENT

REPROJECTION

COMPAREUPDATE RECON

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MLTR

24

validationSiemens Sensation 16

Siemens MLTR

models for iterative reconstruction

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I

iiii yylnyLPoisson Likelihood:

measured data

data computed from current reconstruction image

iy

iy

J

jjijii lexpby

Projection model:

• monochromatic:

iy

bi

models for iterative reconstruction

I

iiii yylnyL

J

jjijii lexpby

waterref

waterk

kk

J

jjijkiki PlPexpby

Poisson Likelihood:

Projection model:

• monochromatic:

• 1 material polychromatic:

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energy k

intensity bik

measured data

data computed from current reconstruction image

iy

iy

energy“water correction”

MLTR_C

models for iterative reconstruction

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J

jjijii lexpby

J

jjkij

K

kiki lexpby

• Full Polychromatic Model – IMPACT

I

iiii yylnyLPoisson Likelihood:

energy k

intensity bik

Projection model:

jk = j ∙ photok + j ∙ Comptonk

models for iterative reconstruction

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J

jjijii lexpby

J

jjkij

K

kiki lexpby

• Full Polychromatic Model – IMPACT

water

Comptonphoto-electric

attenuation

al

jk = photo-electric + Compton at energy k

Comptonk = Klein-Nishina (energy)Photok ≈ 1 / energy3

models for iterative reconstruction

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J

jjijii lexpby

J

jjkij

K

kiki lexpby

• Full Polychromatic Model – IMPACT

and (1/cm)

mono (1/cm)

jk = j ∙ photok + j ∙ Comptonk

jk = j∙ photok + j ∙ Comptonk

and (1/cm)

mono (1/cm)

models for iterative reconstruction

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patches, local models

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MLTR

convex algorithm [1]

[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

patchwork: local update [2,3]

i k kikiij

i iiijjj lyl

yyl

bowtie, BHC

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e-

energy k

intensity bik

• raw CT data not corrected for beam hardening• send spectrum through filter and bowtie

bik = spectrum(k) x bowtie(i)

patches, local models

IMPACT is complex and slow, MLTR and MLTR_C are simpler and faster

Find the metals

PATCH 3

PATCH 2

PATCH 1

Define patches

IMPACT in metalsMLTR_C elsewhere

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PATCH 4

clinical CT (Siemens Sensation 16)Body shaped phantom

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sequential CT (Siemens Sensation 16)Body shaped phantom

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FBP Regular PC PC NMAR

IMPACT PATCH MLTR_C + IMPACT

IMPACT

20 iter x 116 subsets

sequential CT (Siemens Sensation 16)Body shaped phantom

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Black = FBPBlue = PC-NMARRed = IMPACT PATCH

water aluminumCoCr..Ti Al V PMMA water

helical CT

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sequential 2 x 1mm helical 16 x 0.75mm

helical CT

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MIP

IMPACT

FBP

NMAR

metal patches,uniform init.

no patches,NMAR init.

metal patches,NMAR init.

5 iter x 116 subsets

helical CT

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IMPACT

FBP

NMAR

metal patches,uniform init.

no patches,NMAR init.

metal patches,NMAR init.

MIP

helical CT

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FBP NMAR5 it10 it

IMPACT

helical CT

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We give patches same x-y sampling but increased z-sampling:

z-sampling x 3impact, regular z

to do

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• after 5..10 x 100 iterations with patches still incomplete convergence• persistent artifacts near flat edges of metal implants

• we currently think it is noto scattero non-linear partial volume effecto crosstalk, afterglowo detector dead space

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thanks

better physical model

better reconstruction

Katrien Van SlambrouckBruno De Man

Karl Stierstorfer,David Faul, Siemens