1iMinds-Vision Lab, University of Antwerp, Antwerp, Belgium.2Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands.

Gabriel Ramos-Llordén1, Hilde Segers1, Willem J. Palenstijn1,Arnold J. den Dekker1,2 and Jan Sijbers1

Partial discreteness: a new type of prior knowledge for MRI reconstruction

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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

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Partial discreteness: a new type of prior knowledge for MRI reconstruction3417

Partial discreteness model

𝜌1

𝜌2

𝟏𝒜1

𝟏𝒜2

𝒙𝒜

Σ+¿+¿+¿

𝑒𝑖𝚽

𝒜=¿𝑘∈ {1,2 }𝒜𝑘𝑐𝑎𝑟𝑑 (𝒜𝑘 )≫0

Variant intensity class

Phase

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5

Partial discreteness: a new type of prior knowledge for MRI reconstruction3417

Partial discreteness model

𝜌1

𝜌2

𝟏𝒜1

𝟏𝒜2

𝒙𝒜

Σ+¿+¿+¿

𝑒𝑖𝚽

Variant intensity class

Phase

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𝒜=¿𝑘∈ {1,2 }𝒜𝑘𝑐𝑎𝑟𝑑 (𝒜𝑘 )≫0

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Partial discreteness: a new type of prior knowledge for MRI reconstruction3417

Penalized iterative reconstruction

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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

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¿ 𝒙(𝑡 )∨¿

K-Gaussian mixture model fitting [Caballero J., MICCAI 2014]

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2

A posteriori probability maps

Bayes' theorem

Past characterization

1 23

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Partial discreteness: a new type of prior knowledge for MRI reconstruction3417

Bayesian segmentation operator

…

¿ 𝒙(𝑡 )∨¿

13

2 Temporal regularization

Past characterization

𝒙𝑝𝑟𝑜𝑏=�̂�1𝑝1(𝑡 )+ �̂�2𝑝2

(𝑡 )+𝑝3(𝑡 )∘∨𝒙 (𝑡 )∨¿

𝑝1(𝑡 ) 𝑝3

(𝑡 ) 𝑝2(𝑡 )

�̂�1

�̂�2

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1 23

Partial discreteness: a new type of prior knowledge for MRI reconstruction3417

Bayesian segmentation operator

𝒙𝑝𝑟𝑜𝑏

Otsu thresholding

𝒜1

𝒜2 𝒜  

𝒙𝒜 =𝟏𝒜   ∘ 𝒙𝑝𝑟𝑜𝑏

Estimated partially discrete image

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Partial discreteness: a new type of prior knowledge for MRI reconstruction3417

Weights determine where the discreteness error is considered

Bayesian segmentation operator‖𝑾 (𝑡 ) (𝒙−𝒗 (𝑡 ) )‖❑Discreteness error: with

𝑝1(𝑡 ) 𝑝2

(𝑡 ) 𝑝3(𝑡 )

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Partial discreteness: a new type of prior knowledge for MRI reconstruction3417

• Simulations with breast implant and angiography data

• Single coil radial k-space sampling with varying number of spokes,

• Smoothly varying phase added

• Comparison against Conjugate Gradient (CG) with smoothness prior and Total Variation (TV) [Gai.J. et al. (Impatient Toolbox), ISMRM 2012]

Experiments

𝑁 𝑠𝑝𝑜𝑘𝑒𝑠

𝑘𝑥

𝑘𝑦

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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,  

 

 

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Partial discreteness: a new type of prior knowledge for MRI reconstruction3417

Results Breast implant experiment: segmentation metrics

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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,  

 

 

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Partial discreteness: a new type of prior knowledge for MRI reconstruction3417

Conclusions

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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