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Compressed Sensing 4D Flow Reconstruction using
Divergence-free Wavelet Transform
Frank Ong1, Martin Uecker1, Umar Tariq2, Albert Hsiao2, Marcus Alley2, Shreyas Vasanawala2 and
Michael Lustig1
1 University of California, Berkeley2 Stanford University
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 HealthcareType of Relationship: Funding
Declaration ofFinancial Interests or
Relationships
4D Flow MRIProvides anatomical and functional cardiac information in a single acquisition
Ref: Markl et. al JMRI 2003
4D flow showed a regurgitant jet caused by a lesion that could not be well seen on conventional cardiac
MRI
Clinically Viable 4D flow
Want:
1. Reasonable scan time (< 10 minutes)
2. High spatiotemporal resolution for anatomy
Approaches used so far:
• Parallel imaging
• Compressed sensing
• Motion correction
Goal: Reduce Scan Time
Utilize physical property of blood flow in compressed sensing reconstruction
• Blood flow is divergence-free
(What flows in flows out)
Divergence-free Not divergence-free
This Work
1. Divergence-free wavelet transform
2. Phase-wrap tolerant reconstruction
Joint reconstruction of all velocity encodings
Prior Works
• Loecher et. al ISMRM 2014
• Busch et. al MRM 2013
• Song et. al MRM 1994
Compressed Sensing Reconstruction
Data consistency
Wavelet denoising
Better denoising → Better reconstruction
Divergence-free Wavelet Transform• Shown to be effective in denoising 4D flow
data
Divergence-freewavelet
denoising
Ref: Ong et. al MRM 2014
Divergence-free Wavelet Transform• Shown to be effective in denoising 4D flow
data
• “Soft” divergence-free constraint
Ref: Ong et. al MRM 2014
Non-divergence-free component
Compressed Sensing Reconstruction with Divergence-free Wavelet Transform
Data consistency
Spatial wavelet
denoising on magnitude
image
Divergence-free wavelet denoising
on phase images
Ref: Fessler et. al ISBI 2004, Zhao et. al TMI 2013
Compressed Sensing Reconstruction with Divergence-free Wavelet Transform
Phase distortion near phase wraps
Magnitude Reference phase Velocity
Phase Cycle Spinning
• Denoising phase wraps creates small distortions
• Errors accumulate over iterations
Phase Cycle Spinning
• Denoising phase wraps creates small distortions
• Errors accumulate over iterations
+ constantphase
Phase Cycle Spinning
• Denoising phase wraps creates small distortions
• Errors accumulate over iterations
+ constantphase
Phase Cycle Spinning
• Denoising phase wraps creates small distortions
• Errors accumulate over iterations
+ constantphase
Phase Cycle Spinning
• Denoising phase wraps creates small distortions
• Errors accumulate over iterations
Results
L1-ESPIRiT +Spatial Wavelet
L1-ESPIRiT + Divergence-Free Wavelet
Velocity map (SI direction)20 cardiac phasesSize = 256x256x164Resolution~1.15x1.15x1 mmUndersampled by 4
π- π
Results
L1-ESPIRiT +Spatial Wavelet
L1-ESPIRiT + Divergence-Free Wavelet
Speed map20 cardiac phasesSize = 256x256x164Resolution~1.15x1.15x1 mmUndersampled by 4
150 m/s0 m/s
SummaryDivergence-free wavelet transform
Phase cycle spinning
Wavelet code available online:
http://www.eecs.berkeley.edu/~mlustig/Software.html
SummaryDivergence-free wavelet transform
Phase cycle spinning
Wavelet code available online:
http://www.eecs.berkeley.edu/~mlustig/Software.html
Thank you
Supported by
GE Healthcare, NSF Graduate Fellowship, NIH grants P41RR09784, R01EB009690, American Heart Association 12BGIA9660006, and the Sloan Research Fellowship.