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

SummaryDivergence-free wavelet transform

Phase cycle spinning

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.