Iterative reconstruction for metal artifact reduction in CT

transcript

• the problem

• projection completion

• polychromatic ML model for CT

• local models, bowtie,…

• examples

Katrien Van Slambrouck, Johan Nuyts

Nuclear Medicine, KU Leuven

the problem

jj ijlii eby

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

ln(b/y)

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)

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

Energy (keV) Energy (keV)

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, …

µ1µ2

Artifacts in CT

Typical artifact appearance: dark and white streaks connecting edges

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

Artifacts in CT

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

IV. Noise• Quantum nature: ± Poisson distribution

Artifacts in CT

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

• 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

window 600 HU

PMMAH2O

true object FBP projection completion

window 600 HU

• 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

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

sinogram,metals erased

sinogram ofthe segmentedreconstruction

normalizedsinogram,metals erased

interpolatedsinogram

unnormalizedinterpolatedsinogram

proj.completion and NMAR

true object FBP projectioncompletion

window 300 HU

jj ijlii eby

Maximum Likelihood for CT

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

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

p(recon | data) ~

p(data | recon)

projection Poisson

j ijjii lexpby

j = 1..Ji = 1..I

ii )y|y(p

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

p(data | recon)recon data

iii yylnyL(data | recon) j ijjl

ii eby

i k kikiij

i iiijjj lyl

iterative maximisation of L:

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

MEASUREMENT

REPROJECTION

COMPAREUPDATE RECON

validationSiemens Sensation 16

Siemens MLTR

models for iterative reconstruction

iiii yylnyLPoisson Likelihood:

measured data

data computed from current reconstruction image

jjijii lexpby

Projection model:

• monochromatic:

iiii yylnyL

jjijii lexpby

waterref

waterk

jjijkiki PlPexpby

Poisson Likelihood:

Projection model:

• monochromatic:

• 1 material polychromatic:

energy k

intensity bik

measured data

data computed from current reconstruction image

energy“water correction”

MLTR_C

jjijii lexpby

kiki lexpby

• Full Polychromatic Model – IMPACT

iiii yylnyLPoisson Likelihood:

energy k

intensity bik

Projection model:

jk = j ∙ photok + j ∙ Comptonk

jjijii lexpby

kiki lexpby

Comptonphoto-electric

attenuation

jk = photo-electric + Compton at energy k

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

jjijii lexpby

kiki lexpby

and (1/cm)

mono (1/cm)

jk = j ∙ photok + j ∙ Comptonk

jk = j∙ photok + j ∙ Comptonk

and (1/cm)

mono (1/cm)

patches, local models

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

bowtie, BHC

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

PATCH 4

clinical CT (Siemens Sensation 16)Body shaped phantom

sequential CT (Siemens Sensation 16)Body shaped phantom

FBP Regular PC PC NMAR

IMPACT PATCH MLTR_C + IMPACT

IMPACT

20 iter x 116 subsets

sequential CT (Siemens Sensation 16)Body shaped phantom

Black = FBPBlue = PC-NMARRed = IMPACT PATCH

water aluminumCoCr..Ti Al V PMMA water

helical CT

sequential 2 x 1mm helical 16 x 0.75mm

helical CT

IMPACT

metal patches,uniform init.

no patches,NMAR init.

metal patches,NMAR init.

5 iter x 116 subsets

helical CT

IMPACT

metal patches,uniform init.

no patches,NMAR init.

metal patches,NMAR init.

helical CT

FBP NMAR5 it10 it

IMPACT

helical CT

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

z-sampling x 3impact, regular z

• 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

thanks

better physical model

better reconstruction

Katrien Van SlambrouckBruno De Man

Karl Stierstorfer,David Faul, Siemens

Iterative reconstruction for metal artifact reduction in CT

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