Nicolas DUCROS, Simon RIT, Juan FPJ ABASCAL, Bruno SIXOU and Françoise PEYRIN
Biomedical Imaging Research Center
Nonlinear regularized decomposition of spectral
x-ray projection images
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
SPECTRAL CT IMAGING
Conventional vs. Spectral = Grey level vs Color!
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[Cormode et al., Radiology, 256 (3), 2010]
Spectral CT Traditional CT
+ Chemical components + Density (g.cm-3) + K-edge contrast imaging
- Average attenuation - Arbitrary units
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RECONSTRUCTION STRATEGIES
3
Sinogram
object
Tomographic Reconstruction
Linear Attenuation Coefficient
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RECONSTRUCTION STRATEGIES
3
Sinogram
object
Tomographic Reconstruction
Photon Counting Detector
Linear Attenuation Coefficient
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RECONSTRUCTION STRATEGIES
3
Sinogram
object
Tomographic Reconstruction
Photon Counting Detector
Linear Attenuation Coefficient
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RECONSTRUCTION STRATEGIES
3
Sinogram
object
Tomographic Reconstruction
Photon Counting Detector
Linear Attenuation Coefficient
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RECONSTRUCTION STRATEGIES
3
Sinogram
object
Tomographic Reconstruction
Photon Counting Detector
Linear Attenuation Coefficient
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RECONSTRUCTION STRATEGIES
3
Sinogram
object
Tomographic Reconstruction
Spectral
[Mendoca, et al., IEEE TMI, 2014] [Long and Fessler, IEEE TMI, 2014]
[Zhang et al., IEEE TMI, 2014] [Barber, Fully 3D, 2015]
Photon Counting Detector
Material Mass Density
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RECONSTRUCTION STRATEGIES
3
Sinogram
object
Material sinogram
Decomposition
[Alvarez et al., PMB, 1976] [Brody et al., Med. Phys, 1981] [Schlomka et al., PMB, 2007] [Roessl et al., PMB, 2007]
Tomographic Reconstruction
Spectral
[Mendoca, et al., IEEE TMI, 2014] [Long and Fessler, IEEE TMI, 2014]
[Zhang et al., IEEE TMI, 2014] [Barber, Fully 3D, 2015]
Photon Counting Detector
Material Mass Density
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RECONSTRUCTION STRATEGIES
3
Sinogram
object
Material sinogram
Decomposition
[Alvarez et al., PMB, 1976] [Brody et al., Med. Phys, 1981] [Schlomka et al., PMB, 2007] [Roessl et al., PMB, 2007]
Tomographic Reconstruction
[Schirra et al., IEEE TMI, 2014] [Xu et al., PMB, 2014] [Sawatzky et al., IEEE TMI, 2014]
Tomographic Reconstruction
Spectral
[Mendoca, et al., IEEE TMI, 2014] [Long and Fessler, IEEE TMI, 2014]
[Zhang et al., IEEE TMI, 2014] [Barber, Fully 3D, 2015]
Photon Counting Detector
Material Mass Density
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
GOAL AND MOTIVATION
Why material decomposition of the sinogram? 1. Embeds all the nonlinearities of spectral CT 2. Naturally parallelizable across the projection views 3. Applicable to both CT and interventional radiography
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Sinogram Material sinogram
Decomposition
[Alvarez et al., PMB, 1976] [Brody et al., Med. Phys, 1981] [Schlomka et al., PMB, 2007] [Roessl et al., PMB, 2007]
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
GOAL AND MOTIVATION
5
Sinogram Material sinogram
Decomposition
[Alvarez et al., PMB, 1976] [Brody et al., Med. Phys, 1981] [Schlomka et al., PMB, 2007] [Roessl et al., PMB, 2007]
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
GOAL AND MOTIVATION
5
Sinogram Material sinogram
Decomposition
[Alvarez et al., PMB, 1976] [Brody et al., Med. Phys, 1981] [Schlomka et al., PMB, 2007] [Roessl et al., PMB, 2007]
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
GOAL AND MOTIVATION
5
Sinogram Material sinogram
Decomposition
[Alvarez et al., PMB, 1976] [Brody et al., Med. Phys, 1981] [Schlomka et al., PMB, 2007] [Roessl et al., PMB, 2007]
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
GOAL AND MOTIVATION
2D projection images at a fixed view
5
Sinogram Material sinogram
Decomposition
[Alvarez et al., PMB, 1976] [Brody et al., Med. Phys, 1981] [Schlomka et al., PMB, 2007] [Roessl et al., PMB, 2007]
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
GOAL AND MOTIVATION
2D projection images at a fixed view
Notations
5
Sinogram Material sinogram
Decomposition
[Alvarez et al., PMB, 1976] [Brody et al., Med. Phys, 1981] [Schlomka et al., PMB, 2007] [Roessl et al., PMB, 2007]
Projected mass (in g.cm-2) Photon numbers (no units)
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
GOAL AND MOTIVATION
2D projection images at a fixed view
Notations
5
Sinogram Material sinogram
Decomposition
[Alvarez et al., PMB, 1976] [Brody et al., Med. Phys, 1981] [Schlomka et al., PMB, 2007] [Roessl et al., PMB, 2007]
Projected mass (in g.cm-2) Photon numbers (no units)
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
CONTRIBUTION
Variational framework Nonlinear decomposition Regularized decomposition
Gauss-Newton algorithm
Gold standard Superlinear convergence rates
6
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
CONTRIBUTION
Descent direction computation
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N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
CONTRIBUTION
Descent direction computation
Study case o M = 3 o P = 256 x 256
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Size
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
CONTRIBUTION
Descent direction computation
Study case o M = 3 o P = 256 x 256
Storage of the full Hessian is intractable!
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Size
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
CONTRIBUTION
Descent direction computation
Study case o M = 3 o P = 256 x 256
Storage of the full Hessian is intractable! Hessian is block diagonal with only PM2 non zero entries
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Size
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
NUMERICAL SIMULATIONS
Forward model
8
[Schlomka et al., PMB, 2008]
[Poludniowski et al., Med Phys, 2007]
4 bins
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
NUMERICAL SIMULATIONS
Forward model
8
[Schlomka et al., PMB, 2008]
[Poludniowski et al., Med Phys, 2007]
4 bins
Elekta Synergy
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
NUMERICAL SIMULATIONS
Forward model
8
[Schlomka et al., PMB, 2008]
[Poludniowski et al., Med Phys, 2007]
4 bins
Elekta Synergy
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
NUMERICAL SIMULATIONS
Numerical Phantom 3-material Thorax Phantom
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3D atlas (labels) [Kéchichian et al., IEEE TIP, 2013]
3D volumes (g.cm-3)
Projection (RTK) http://www.openrtk.org/
2D image (g.cm-2)
3D CT scan (a.u) [3D-IRCADb data set]
Materials • Soft tissue • Bone • Gadolinium
(Portal vein )
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RESULTS
A typical decomposition Weighted least squares
Material-dependent regularization
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N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RESULTS
A typical decomposition Weighted least squares
Material-dependent regularization
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N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RESULTS
Convergence of the algorithm
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N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RESULTS
Convergence of the algorithm
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N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RESULTS
Influence of noise
Poisson noise
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N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RESULTS
Influence of noise
Poisson noise
Error vs noise
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N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RESULTS
Influence of noise
Poisson noise
Error vs noise
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N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RESULTS
Influence of noise
Poisson noise
Error vs noise
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N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RESULTS
Influence of the marker concentration
Concentration range: 0.01 to 1 g.cm-3
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N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RESULTS
Influence of the marker concentration
Concentration range: 0.01 to 1 g.cm-3
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N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RESULTS
Influence of the marker concentration
Concentration range: 0.01 to 1 g.cm-3
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N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
CONCLUSION
Material decomposition
We proposed a GN algorithm Weighted least squares L2/L1 material dependent
regularization
Thorax phantom with portal vein marked with gadolinium Different number of counts Different marker concentrations
Encouraging results
Fast convergence Good reconstruction quality
Thanks to the spectral CT team Juan FPJ ABASCAL Tom HOHWEILLER Jean-Michel LÉTANG Cyril MORY Françoise PEYRIN Odran PIVOT Simon RIT Bruno SIXOU Gloria VILCHES FREIXAS
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THANK YOU FOR
YOUR ATTENTION
N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RESULTS
Convergence Stopping criteria
o Step Length
o Cost function decrease
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N. Ducros, 19.07.2017 | CT Meeting – Spectral Session
RESULTS
Choice of the regularization parameter
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