ML reconstruction for CT - University of Sydney · Dual energy CT: exploits dependence of linear attenuation coefficient on photon energy to discriminate between materials. 42 . 22

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ML reconstruction for CT

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• derivation of MLTR

• rigid motion correction

• resolution modeling

• polychromatic ML model

• dual energy ML model

Bruno De Man, Katrien Van Slambrouck, Maarten Depypere, Frederik Maes,

Jung-ha Kim, Roger Fulton, Johan Nuyts

MIRC, KU Leuven & Univ of Sydney

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Tomography

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CT

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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

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Maximum Likelihood

p(recon | data) ~

p(data | recon)

projection Poisson

µj

j = 1..J i = 1..I

ln(p(data | recon)) = L(data | recon) = ~

p(data | recon) recon data

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Maximum Likelihood

L(data | recon)

find recon:

Iterative inversion needed

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MLTR

7 µ

L(µ+Δµ)

Likelihood

T1(µ, Δµ)

MLTR

8 µ

L(µ+Δµ)

T1(µ, Δµ)

Likelihood

T2(µ, Δµ)

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MLTR

9 µ

L(µ+Δµ)

T1(µ, Δµ)

Likelihood

T2(µ, Δµ) T1(µ, Δµ)

MLTR

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T1(µ, Δµ) T2(µ, Δµ)

L(µ+Δµ)

Likelihood

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MLTR

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MLTR

MEASUREMENT

REPROJECTION

COMPAREUPDATE RECON

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MLTR

FBP

MLTR

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MLTR

FBP

MLTR

metal artifact reduction projection truncation

FBP

MLTR

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MLTR for rigid motion correction

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1) validation Siemens Sensation 16

Siemens MLTR

J-H Kim, Z Kuncic, R Fulton, J Nuyts

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MLTR for rigid motion correction 2) simulation

rotations: •  in transaxial plane •  in sagittal plane •  in coronal plane

translations: •  along column •  along row •  along plane

trans

cor

sag proj

software phantom

CT protocol

•  high pitch •  narrow collimation •  low tube current •  high rotation speed

low dose

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motion 5 s measured rat motion


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MLTR modified to support •  stationary object •  rigid view-dependent displacement of CT detector-source assembly

“relativity”: assign inverse motion to CT

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pitch = 2

trans cor sag proj MLTR w/o correction

MLTR with correction

MLTR w/o correction

MLTR with correction

pitch = 0.5


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3) phantom measurement

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MLTR

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MLTR

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MLTR

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MLTR

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Ex vivo -‐ global FBP -‐ global FBP -‐ adap1ve MAPTR global

Recon

Segment

microCT

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metal artifacts

Double hip prosthesis Double knee prosthesis Dental fillings

Cause of metal artifacts: •  Beam hardening •  Scatter •  (Non) linear partial volume effects •  Noise •  (Motion)

Mouse bone and titanium screw (microCT)

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metal artifact reduction (MAR)

Projection completion   Initial filtered backprojection (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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Models for iterative reconstruction

SKYSCAN SPECTRUM Black = without filter Blue = 0.5 mm Al and 0.038 mm Cu

Poisson Likelihood:

Update:

Projection model:

•  monochromatic:

•  1 material polychromatic:

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•  Full Polychromatic Model – IMPACT



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Material dependence

Energy dependence

•  Full Polychromatic Model – IMPACT

Base substances

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Base substances

Φ a

nd θ

(1/c

m)

µmono (1/cm)

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 metals MLTR_C elsewhere

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simulations

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Geometry based on Siemens Sensation 16 Included:

•  polychromatic spectrum •  detector, source and view subsampling •  afterglow •  crosstalk

source

detector view(k) = a*view(k-1) + (a-1)*view(k)

500 µs

results

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PMMA Al

Fe

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clinical CT (Siemens Sensation 16) Circular phantom

PMMA Al

Fe

Siemens Sensation 16 (part of Biograph 16 PET/CT)

•  120 kV, 300 mA •  2 x 1.00 mm •  Circular scan, 0.5 s per rotation

(no flying focal spot) •  2D reconstruction of 1 slice

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clinical CT (Siemens Sensation 16) Body shaped phantom

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clinical CT (Siemens Sensation 16) Body shaped phantom

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iterative reconstruction for microCT

FDK IMPACT


Ti-cage, culture of soft tissue and cartilage 40

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Dual energy CT

Dual energy CT has been widely used to discriminate bone from contrast agent.

Dual energy CT: exploits dependence of linear attenuation coefficient on photon energy to discriminate between materials.

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Dual energy microCT applications

MicroCT: imaging bone and contrast agents in small animals, such as mice. Bone development and repair requires a normal vascular system to supply oxygen and nutrients.

MicroCT Imaging X-ray energy range: 20 – 100 keV

Rat skull Mouse bone fracture Detail of trabecular bone structure

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Post-reconstruction: microCT

post-reconstruction dual energy for microCT problems:

  beam hardening due to dense materials contrast agent metal implants

  Noise. Signal-to-noise ratio is limited by In vivo microCT: dose concerns Ex vivo microCT: cumbersome long scan times

Perfused mouse tibia E1: 56 minutes

Noise robustness can be increased by   incorporating a noise model   resorting to statistical approaches

Voxel by voxel comparison is sensitive to erroneous intensity values

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Polychromatic attenuation model

Bone Water

Dual energy algorithms exploit the dependency of the linear attenuation coefficient µ on the photon energy E The attenuation can be modeled as a linear combination of b basis functions

A well known combination of basis functions is the Compton scatter and the photoelectric effect.

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IMPACT extension to dual energy microCT

Iodine Iodine

Our model consists of a third basis function that models the attenuation of a single contrast material (barium, iodine, lead):

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Results – Noiseless simulation

Beam hardening affects tissue decomposition

Polychromatic model accounts for beam hardening

Noiseless simulation of water, bone and 0.15 and 0.20 g/ml mixtures of barium sulfate

Post reconstruction

Iterative Decomposition 0.1957 g/ml + 0.0024 (0.20)

0.1455 g/ml + 0.0021 (0.15)

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Noisy

Coefficient of variation in BaSO4 region: 0.36

Coeffecient of variation in BaSO4 region: 0.15

Measurement of polypropene tube, water, bone equivalent material CaHA and a barium sulfate mixture

Post reconstruction

IMPACT Decomposition

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Measurement of a mouse bone perfused with barium sulfate

Post reconstruction Barium fractions

Iterative decomposition Barium coefficients

Iterative decomposition Coloured overlay

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thanks

Documents

ML reconstruction for CT - University of Sydney · Dual energy CT: exploits dependence of linear attenuation coefficient on photon energy to discriminate between materials. 42 . 22