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: frankong@berkeley.edu 1 University of California, Berkeley 2 Stanford University

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

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 ----- Meeting Notes (5/22/15 12:06) ----- 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

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 # 0575 Multi-scale Low Rank MRI

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

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

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

This Work: Multi-scale Low Rank MRI Combines all three methods Captures all scales of dynamics Locally Low Rank Globally Low Rank Sparse # 0575 Multi-scale Low Rank MRI

Multi-scale Low Rank MRI Decomposition Fully-Sampled Dataset 1x1 4x4 16x16 + + = + 64x64 128x112 # 0575 Multi-scale Low Rank MRI

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

Illustration of the iterative reconstruction Time kspace Can be formally derived using ADMM # 0575 Multi-scale Low Rank MRI

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

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

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 # 0575 Multi-scale Low Rank MRI

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 # 0575 Multi-scale Low Rank MRI

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 # 0575 Multi-scale Low Rank MRI

= 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) http://www.eecs.berkeley.edu/~mlustig/Software.html = + Thank You! 64x64 128x112 # 0575 Multi-scale Low Rank MRI