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1iMinds-Vision Lab, University of Antwerp, Antwerp, Belgium.2Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands.
Gabriel Ramos-LlordΓ©n1, Hilde Segers1, Willem J. Palenstijn1,Arnold J. den Dekker1,2 and Jan Sijbers1
Partial discreteness: a new type of prior knowledge for MRI reconstruction
β¦
12
3Bayes' theorem
1 2 3
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
Some regions are approximately constant in intensity
Partial discrete images: piece-wise constant part + texture part
Partial discreteness as a prior for ill-posed reconstruction problems
IntroductionBreast implant Dental MRI FLAIR sequences Angiography
1/12
1 2 3 4
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
Partial discreteness model
π1
π2
ππ1
ππ2
ππ
Ξ£+ΒΏ+ΒΏ+ΒΏ
πππ½
π=ΒΏπβ {1,2 }ππππππ (ππ )β«0
Variant intensity class
Phase
2/12
5
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
Partial discreteness model
π1
π2
ππ1
ππ2
ππ
Ξ£+ΒΏ+ΒΏ+ΒΏ
πππ½
Variant intensity class
Phase
3/12
π=ΒΏπβ {1,2 }ππππππ (ππ )β«0
6
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
Penalized iterative reconstruction
4/12
Discreteness error
iteratively estimated partial discrete imagespatially-variant weight diagonal matrix
k-space data
Fourier matrix
image Regularization parameter
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
Bayesian segmentation operator
β¦
ΒΏ π(π‘ )β¨ΒΏ
K-Gaussian mixture model fitting [Caballero J., MICCAI 2014]
13
2
A posteriori probability maps
Bayes' theorem
Past characterization
1 23
5/12
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
Bayesian segmentation operator
β¦
ΒΏ π(π‘ )β¨ΒΏ
13
2 Temporal regularization
Past characterization
πππππ=οΏ½ΜοΏ½1π1(π‘ )+ οΏ½ΜοΏ½2π2
(π‘ )+π3(π‘ )ββ¨π (π‘ )β¨ΒΏ
π1(π‘ ) π3
(π‘ ) π2(π‘ )
οΏ½ΜοΏ½1
οΏ½ΜοΏ½2
5/12
1 23
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
Bayesian segmentation operator
πππππ
Otsu thresholding
π1
π2 π
ππ =ππ β πππππ
Estimated partially discrete image
6/12
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
Weights determine where the discreteness error is considered
Bayesian segmentation operatorβπΎ (π‘ ) (πβπ (π‘ ) )ββDiscreteness error: with
π1(π‘ ) π2
(π‘ ) π3(π‘ )
7/12
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
β’ Simulations with breast implant and angiography data
β’ Single coil radial k-space sampling with varying number of spokes,
β’ Smoothly varying phase added
β’ Comparison against Conjugate Gradient (CG) with smoothness prior and Total Variation (TV) [Gai.J. et al. (Impatient Toolbox), ISMRM 2012]
Experiments
π π πππππ
ππ₯
ππ¦
8/12
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
Results
(a) CG + smoothness (b) CG + TV (c) Proposed
SNR=100
Recovered images and implant contour detection
Breast implant experiment
SNR=100,
9/12
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
Results Breast implant experiment: segmentation metrics
10/12
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
Results Angiography experiment
(a)Original (b)CG + smoothness (c)CG+TV (d)Proposed
SNR=100,
11/12
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
Conclusions
12/12
Partial discreteness prior More detailed reconstructed images
Segmentation benefits from partial discreteness
Thanks for your attention!
Contact: http://visielab.uantwerpen.be/people/gabriel-ramos-llorden
Partial discreteness: a new type of prior knowledge for MRI reconstruction3417
Image references1. Radiopedia.org2. http://www.drbicuspid.com/3. www.reviewofoptometry.com4. https://www.healthcare.siemens.com/5. https://www.healthcare.siemens.com/magnetic-resonance-imaging/
options-and-upgrades/clinical-applications/advanced-angio6. M Maijers, PhD Thesis