1. Contact: frankong@berkeley.edu
Beyond Low Rank + Sparse: Multi-scale Low Rank Reconstruction for Dynamic Contrast Enhanced Imaging
Frank Ong1, Tao Zhang2, Joseph Cheng2, Martin Uecker1 and Michael Lustig1
Contact:
1 University of California, Berkeley
2 Stanford University

2. Declaration of Financial Interests or Relationships
Speaker Name: Frank Ong I have the following financial interest or relationship to disclose with regard to the subject matter of this presentation: Company Name: GE Healthcare Type of Relationship: Research Support

3. 3D Dynamic Contrast Enhanced (DCE) MRI
Detect and characterize lesions
Any imaging plane and any time point
Challenges with 3D DCE-MRI
DCE imaging has become a popular imaging technique to detect and characterize lesions
3D DCE MRI can further allow radiologists to obtain these information at any imaging plane and any given time point
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bleeding, labeling
Huge amount of data in a fixed time window
Tradeoff between spatial and temporal resolution
3D DCE Dataset
# 0575 Multi-scale Low Rank MRI

4. Goal
Capture true contrast dynamics of DCE …we don’t need to achieve high spatiotemporal resolution for everything
DCE contrast dynamics are structured:
Fast and sparse blood vessel dynamics
Locally correlated kidney and liver dynamics
Stationary smooth tissues
3D DCE Dataset
A multi-scale low rank reconstruction to capture these structured dynamics
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5. Previous works Globally Low Rank [1] Time
Captures globally correlated dynamics
Very sensitive to local dynamics
Low
Rank
Space
[1] Pedersen et al. 2009, Liang et al. ISBI 2006
[2] Ricardo et al. MRM 2014, Chandrasekaran et al. SIAM J. Optim., Candes et al. J ACM 2011
# 0575 Multi-scale Low Rank MRI
[3] Lingala et al. TMI 2011, Trzasko et al, ISMRM 2011, Zhang et al. MRM 2015

6. Previous works Globally Low Rank [1] Low Rank + Sparse [2] + Time
Captures globally correlated dynamics
Very sensitive to local dynamics
Low Rank + Sparse [2]
Captures global + sparse dynamics
Many dynamics are not sparse!
Low
Rank +
Space
[1] Pedersen et al. 2009, Liang et al. ISBI 2006
[2] Ricardo et al. MRM 2014, Chandrasekaran et al. SIAM J. Optim., Candes et al. J ACM 2011
# 0575 Multi-scale Low Rank MRI
[3] Lingala et al. TMI 2011, Trzasko et al, ISMRM 2011, Zhang et al. MRM 2014

7. Previous works Globally Low Rank [1] Low Rank + Sparse [2]
Time
Globally Low Rank [1]
Captures globally correlated dynamics
Very sensitive to local dynamics
Low Rank + Sparse [2]
Captures global + sparse dynamics
Many dynamics are not sparse!
Locally Low Rank [3]
Captures local correlated dynamics
Does not use global correlation
Space
[1] Pedersen et al. 2009, Liang et al. ISBI 2006
[2] Ricardo et al. MRM 2014, Chandrasekaran et al. SIAM J. Optim., Candes et al. J ACM 2011
# 0575 Multi-scale Low Rank MRI
[3] Lingala et al. TMI 2011, Trzasko et al, ISMRM 2011, Zhang et al. MRM 2014

8. This Work: Multi-scale Low Rank MRI
Combines all three methods
Captures all scales of dynamics
Locally
Low Rank
Globally
Low Rank
Sparse
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9. Multi-scale Low Rank MRI Decomposition
Fully-Sampled Dataset
1x1
4x4
16x16 + + = +
64x64
128x112
# 0575 Multi-scale Low Rank MRI

10. Illustration of the iterative reconstruction
Time
kspace
# 0575 Multi-scale Low Rank MRI

11. Illustration of the iterative reconstruction
Time
kspace
Can be formally derived using ADMM
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12. Goodies of the Multi-scale Low Rank
Convex program -> always converges
Theoretically guided thresholds:
Low Rank + Sparse: ~1 for sparse, image size for low rank
Multi-scale Low Rank: ~ block size
Computationally efficient:
At most 2x more computation than conventional low rank methods
# 0575 Multi-scale Low Rank MRI

13. Comparison Results Globally Low Rank Low Rank + Sparse
Compressed sensing (Poisson Disk) undersampling [1]
Parallel Imaging (ESPIRiT) [2]
Free-breathing Respiratory Soft-gated (Butterfly Navigator) [3]
Resolution: 1x1.4x2 mm3 and ~8s
Globally Low Rank
Low Rank + Sparse
Locally Low Rank
Multi-scale Low Rank
[2] Uecker et al. MRM 2014, [3] Cheng et al. JMRI 2014, Zhang et al. JMRI 2013
# 0575 Multi-scale Low Rank MRI

14. Comparison Results Globally Low Rank Low Rank + Sparse
Compressed sensing (Poisson Disk) undersampling [1]
Parallel Imaging (ESPIRiT) [2]
Free-breathing Respiratory Soft-gated (Butterfly Navigator) [3]
Resolution: 1x1.4x2 mm3 and ~8s
Globally Low Rank
Low Rank + Sparse
Locally Low Rank
Multi-scale Low Rank
[1] Uecker et al. MRM 2014, [2] Cheng et al. JMRI 2014
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15. Comparison Results Locally Low Rank Globally Low Rank
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temporal curves, bleeding
Low Rank + Sparse
Multi-scale Low Rank
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16. Comparison Results Locally Low Rank Globally Low Rank
----- Meeting Notes (5/22/15 11:53) -----
temporal curves, bleeding
Low Rank + Sparse
Multi-scale Low Rank
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17. = Conclusion: + + + Berkeley Advanced Reconstruction Toolbox (BART)
Multi-scale low rank reconstruction
Captures the right dynamics at the right scale
Generalizes low rank + sparse
1x1
4x4
16x16 + +
Berkeley Advanced Reconstruction Toolbox (BART) = +
Thank You!
64x64
128x112
# 0575 Multi-scale Low Rank MRI