OptimizedCS-Waveimagingwithtailoreddata-samplingandefficientreconstruction

BBilgic,HYe,LLWald,KSetsompop

MartinosCenterforBiomedicalImaging,Charlestown,MA,USADepartmentofRadiology,HarvardMedicalSchool,Boston,MA,USA

Speaker Name: Berkin Bilgic

I have no financial interests or relationships to disclose with regard to the subject matter of this presentation.

Declaration ofFinancial Interests or Relationships

§Wave-CAIPImodifies3DGREtrajectorytofollowacorkscrewalongeachreadoutline[1]

§ Foracceleratedacquisitions,thisspreadsthealiasinginall3Ddimensionstosubstantiallyimproveparallelimaging

§ Acquisitionhasthesameoff-resonancecharacteristicasNormalGRE(voxelshiftinreadout),andreconisfullyCartesian

Kx

Kz

Ky

Wave-CAIPItrajectory

R=2accelerationinKyAliasingvoxelsarespreadouttoincreasethevariationincoilsensitivityprofiles:

ImprovedG-Factor

y

x

aliasingvoxelsarefurtheraparttwovoxelscollapseNormalGRE Wave-CAIPI

[1] B Bilgic, MRM’14

Wave-CAIPIfor3D-GRE

§ RecentlyintroducedCS-Wave[1]employedPoissonsamplingandWaveletpenaltytocombineCompressedSensingwithWaveencoding

§WeproposeoptimizedCS-Wavewithv EfficientADMMreconstruction

v TotalVariationregularization

v Tailoreddata-sampling

§Whencombined,thesedoubletheimprovementachievedbythepreviousCS-Wave

§ Providing20%RMSEreductionoverWave-CAIPIat15-foldaccl

CompressedSensingWave§

[1]ATCurtisetal,ISMRM’15

CompressedSensingWave

[1]ATCurtisetal,ISMRM’15[2]HYeetalISMRM’16p3246

§ RecentlyintroducedCS-Wave[1]employedPoissonsamplingandWaveletpenaltytocombineCompressedSensingwithWaveencoding

§WeproposeoptimizedCS-Wavewithv EfficientADMMreconstruction

v TotalVariationregularization

v Tailoreddata-sampling

§ CombiningCS-WavewithSimultaneousMultiSlice(SMS)Echo-Shiftstrategy[2]furtherincreasestheaccelerationto30-fold(15×2)

§ EnablingQuantitativeSusceptibilityMapping(QSM)from3headorientationsatlongTEand1.5mmisoin72sec(24sec/orientation)

§ Despitefollowinganon-Cartesiantrajectory,WaveencodingcanbeexpressedinCartesianspacethroughpointspreadfunction(psf):

WaveRecon:ForwardModel

WaveImage(iDFTwithout gridding)

m(x, y) wave(x, y)

Underlying Imagepsf (x, y0 )

y

x

wave(x, y) = psf(x, y)⊗m(x, y)

§

WaveRecon:ForwardModel

WaveImage(iDFTwithout gridding)

m(x, y) wave(x, y)

Underlying Imagepsf (x, y0 )

y

x

wave(x, y) = FxH ⋅Psf(kx, y) ⋅Fx ⋅m(x, y)

Noneedforgridding,simpleDFT

§ Despitefollowinganon-Cartesiantrajectory,WaveencodingcanbeexpressedinCartesianspacethroughpointspreadfunction(psf):

§ Extendto3DusingbothGy andGz sinusoidalgradientwaveforms:

WaveRecon:ForwardModel

wave(x, y, z) = FxH ⋅Psf(kx, y, z) ⋅Fx ⋅m(x, y, z)

§§ Andgoto3Dk-spacebyapplyingDFTtobothsides:

WaveRecon:ForwardModel

Fxyz ⋅wave(x, y, z) = Fyz ⋅Psf(kx, y, z) ⋅Fx ⋅m(x, y, z)

WaveRecon:ForwardModel

k = Fyz ⋅Psf ⋅Fx ⋅m

§ Andgoto3Dk-spacebyapplyingDFTtobothsides:

§ IncludecoilsensitivitiesandundersamplingmasktoobtaintheforwardSENSEmodel

WaveRecon:ForwardModel

k =M ⋅Fyz ⋅Psf ⋅Fx ⋅S ⋅m

§

WaveRecon:ForwardModel

k =M ⋅E ⋅m

encoding E = Fyz ⋅Psf ⋅Fx ⋅S

§ IncludecoilsensitivitiesandundersamplingmasktoobtaintheforwardSENSEmodel

§§ RegularizedleastsquarestoincorporateCompressedSensing:

EfficientCS-WaveRecon

1/ 2 k −M ⋅E ⋅m2

2 + λ R ⋅m1

§ Forefficientoptimization,weadoptADMM[1,2]andintroduceauxiliaryvariablesfordataconsistencyandregularizationterms:

§ Thisallowsustoseparatethedifficult3Doptimizationproblemintosmaller

subproblems thataresolvedinclosedformforc andr

1/ 2 k −M ⋅E ⋅m2

2 + λ R ⋅m1

EfficientCS-WaveRecon

c = E ⋅m r = R ⋅m

[1] S Boyd et al, Found Trends Mach Learn’10[2] T Goldstein et al, SIAM J Imaging Sci’09

§

§ Forefficientoptimization,weadoptADMM[1,2]andintroduceauxiliaryvariablesfordataconsistencyandregularizationterms:

§ Andtheimageupdateisfoundbyasimplelinearcombinationofdataconsistencyandregularization

EfficientCS-WaveRecon

[1] S Boyd et al, Found Trends Mach Learn’10[2] T Goldstein et al, SIAM J Imaging Sci’09

(α ⋅S2 +β ⋅R2) ⋅m =α ⋅EH (c− dc )+β ⋅RH (r − dr )

1/ 2 k −M ⋅E ⋅m2

2 + λ R ⋅m1

c = E ⋅m r = R ⋅m

dc & dr : dual variables

§

α & β: Lagrange parameters

EfficientCS-WaveRecon

[1] S Boyd et al, Found Trends Mach Learn’10[2] T Goldstein et al, SIAM J Imaging Sci’09

(α ⋅S2 +β ⋅R2) ⋅m =α ⋅EH (c− dc )+β ⋅RH (r − dr )

1/ 2 k −M ⋅E ⋅m2

2 + λ R ⋅m1

c = E ⋅m r = R ⋅m

R2 = I for WaveletS2 = SoS of sensitivities

§ Forefficientoptimization,weadoptADMM[1,2]andintroduceauxiliaryvariablesfordataconsistencyandregularizationterms:

§ Andtheimageupdateisfoundbyasimplelinearcombinationofdataconsistencyandregularization:closed-formforWavelet

EfficientCS-WaveRecon

[1] S Boyd et al, Found Trends Mach Learn’10[2] T Goldstein et al, SIAM J Imaging Sci’09

1/ 2 k −M ⋅E ⋅m2

2 + λ R ⋅m1

c = E ⋅m r = R ⋅m

m = (α ⋅S2 +β ⋅ I)−1 ⋅ α ⋅EH (c− dc )+β ⋅RH (r − dr )⎡⎣ ⎤⎦

§ Forefficientoptimization,weadoptADMM[1,2]andintroduceauxiliaryvariablesfordataconsistencyandregularizationterms:

§ Andtheimageupdateisfoundbyasimplelinearcombinationofdataconsistencyandregularization:closed-formforWavelet

EfficientCS-WaveRecon

[1] S Boyd et al, Found Trends Mach Learn’10[2] T Goldstein et al, SIAM J Imaging Sci’09

(α ⋅S2 +β ⋅R2) ⋅m =α ⋅EH (c− dc )+β ⋅RH (r − dr )

1/ 2 k −M ⋅E ⋅m2

2 + λ R ⋅m1

c = E ⋅m r = R ⋅m

diag(R2 ) = 6 ⋅ I for TV since Laplacian(α ⋅S2 + 6β ⋅ I)−1: diagonal preconditioner

§ Forefficientoptimization,weadoptADMM[1,2]andintroduceauxiliaryvariablesfordataconsistencyandregularizationterms:

§ Andtheimageupdateisfoundbyasimplelinearcombinationofdataconsistencyandregularization:PreconditionedConjugateGradientforTotalVariation

8.6%RMSE

Proposed:CS-Wave

WaveencodingwithR=15accl@7T

§ Res =1x1x2mm3

§ FOV =224x222x120mm3 tight§ TE/TR=10.9/27ms§ ESPIRiT[1]sensitivitiesfrom16x16x16points§ Hybridsampling[2]: Center25%w/R=3x3Caipi

Outer 75%w/VDPoisson§ Tacq =25sec

hybridsampling

kz

ky

[1] M Uecker et al MRM’14[2] K Sung et al MRM’13

TotalR=15-fold

8.6%RMSE

Proposed:CS-Wave

WaveencodingwithR=15accl@7T

Wave-CAIPI

10.2%RMSE

caipisampling

kz

ky

Recon8.4min

Recon1.8min

hybridsampling

kz

ky

WaveencodingwithR=15accl@3T

7.4%RMSE

Proposed:CS-Wave

Wave-CAIPI

8.9%RMSE

§ Tacq =24sec§ TE/TR=13.3/26ms

Phase&QSMwithR=15accl@7T

-0.038ppm 0.043ppm

-0.09ppm 0.13ppm

Proposed:CS-WaveTissuePhaseV-SHARP[1,2]

[1] F Schweser et al NIMG’11[2] B Wu et al MRM’11

SusceptibilityMapSingle-StepTGV[3]

[3] I Chatnuntawech et al ISMRM’16, p.869 Thu 10:30 Sparse Road to Quantitative Imaging

-0.09ppm 0.13ppm

Phase&QSMwithR=15accl@7T

Wave-CAIPITissuePhase

-0.038ppm 0.043ppm

SusceptibilityMapSingle-StepTGV[3]

[3] I Chatnuntawech et al ISMRM’16, p.869 Thu 10:30 Sparse Road to Quantitative Imaging

Phase&QSMwithR=15accl@3T

-0.038ppm 0.043ppm

-0.09ppm 0.13ppm

TissuePhase

Proposed:CS-Wave

SusceptibilityMapSingle-StepTGV[3]

[3] I Chatnuntawech et al ISMRM’16, p.869 Thu 10:30 Sparse Road to Quantitative Imaging

Phase&QSMwithR=15accl@3T

-0.038ppm 0.043ppm

-0.09ppm 0.13ppm

TissuePhase

Wave-CAIPI

SusceptibilityMapSingle-StepTGV[3]

[3] I Chatnuntawech et al ISMRM’16, p.869 Thu 10:30 Sparse Road to Quantitative Imaging

Echo-Shift§ ForSWIandQSM,longTEisdesiredtobuildupphaseandT2*contrast,whichleadstolongTRandacquisitiontime

§ Echo-shiftexploitstheunusedsequencetimeandinterleavesmultipleechoswithinasingleTRandimprovesefficiencyin2D[1]or3D[2]acquisitions

§ Echo-shifthasalsobeenusedforfMRI(PRESTO)[3],andcombinedwith(SMS)[4]forfurtheracceleration for2Dimaging

§

[1] CTW Moonen et al MRM’92[2] YJ Ma et al MRM’15[3] G Liu et al MRM’93[4] R Boyacioğlu et al SMS Workshop’15

SlabSelectConventional3Dencoding

Multi-SlabEcho-Shiftfor3Dimaging

RF

Gslice

Gread

Gphase

Slab1

TR

§ Conventional3D-GRE:substantialunusedtimeduetolateTR

longTE

acquisition

RF

Slab1 Slab2

Multi-SlabEcho-Shift

Gslice

Gread

TRGphase

Multi-SlabEcho-Shiftfor3Dimaging§Multi-SlabEcho-Shift:addasecondreadoutandcrushergradientsforfasterencoding

Slab1 Slab2

v Slabboundaryartifactv Accelerationinhead-footmoredifficultsincedistancebetweenaliasingvoxelsreduced

byhalf

acquisition

RF

OddSlc EvenSlc

SMSEcho-Shift

Gslice

Gread

TRGphase

SMSEcho-Shiftfor3Dimaging§ SMSEcho-Shift[1]:exciteandencodecombslicegroups

OddSlc EvenSlc

[1]HYeetalISMRM’16p3246

MultiBandRF

acquisition

Echo-ShiftCS-WavewithR=15×2accl@3T

§ 1.5mmiso§ LongTE=35ms (TR=47ms)§ Tacq =24sec

Left Neutral Right

Echo-ShiftCS-WavewithR=15×2accl@3T

QSMfrom3orientations:Ttotal =72secLeft Neutral Right

§ Combineinformationfrom3headorientationstosolveQSMinverseproblem[1]

[1] T Liu et al MRM’09

-0.09ppm 0.11ppm

Echo-ShiftCS-WavewithR=15×2accl@3T

QSMfrom3orientations:Ttotal =72sec

-0.09ppm 0.11ppm

Left Neutral Right

TissuePhase

-0.035ppm 0.035ppm

Conclusion§WeproposedoptimizedCS-Wavewithefficientreconstructionandtailoreddata-sampling

§ SMSEcho-Shiftstrategyutilizestheunusedsequencetimeforextraencoding

§ CombiningCS-WavewithSMSEcho-Shiftpermits30-fold(15×2)acceleration

§ ThisenablesrapidSWIandQSMacquisitionatlongTErequiredforoptimalcontrast

§ Questions/Comments:berkin@nmr.mgh.harvard.edu

§ Support:NIHR24MH106096,R01EB020613,R01EB017337,U01HD087211