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Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department of Radiological Sciences [email protected] 310-267-6838

Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

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Page 1: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing

Peng Hu, Ph.D. Associate Professor

Department of Radiological Sciences [email protected]

310-267-6838

Page 2: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

MRI...

● MRI has low signal levels – Polarization is PPM

● Overcome with higher fields – Improve detection

● High quality coil arrays ● Mostly body noise limited today

● MRI is slow... – Slow to encode

● Compare to digital camera! – Slow repetition times

● Relaxation time constants are long – Need contrast agents – Need faster gradients (1990s)

● Gradients are near optimal today

Page 3: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Gradient Encoding

● One-to-one correspondence between k-space location and MRI signal

● Speed of MRI is dependent on speed of travel in k-space

● K-space location is controlled by gradients ● One MRI signal sample at a time!

– larger volume coverage -> longer scan time

S

Page 4: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Waitaminute…

● Can we increase the speed we travel in k-space using higher gradients and faster switching?

● Yes, you can, but… – Peripheral nerve stimulation – Gradient amplifier power considerations – SNR considerations

NominalSlow Faster

Page 5: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

PeripheralNerveStimulation

● Switching of gradients -> time-varying magnetic field -> electrical current -> nerve stimulation -> tingling sensation

● PNS is not dangerous, but can be disturbing ● FDA limits PNS in MRI systems -> limits in

switching speed of gradients ● Common Max slew rate: 200mT/m/ms

Page 6: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

GradientAmplifier

● Gradient amplifiers feed large electrical currents into the gradient coil

● Gmax ∝ Current [I, amps] ● Slewrate ∝ Voltage [V, volts] ● Power=IV ● R-fold acceleration requires

● R-fold increase in Gmax ● R2-fold increase in slewrate ● Power=IV∝R3!!!

Page 7: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

SNRLoss

● Larger sampling bandwidth -> Larger anti-aliasing filter BW -> allowing more noise power into MRI signal -> decreasing SNR!

● Common Max Sampling Rate: 500KHz (2us period)

Page 8: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

AlternativeTechniquetoSpeedupMRI

● Reduce k-space samples

Parallel Imaging!

Page 9: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

WhyMRIusingCoilArrays

● Increased SNR

Page 10: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

SourcesofNoiseinMRI

● Human Body – Noise from human body is most significant at

high field ● Electronics

– Coils, Pre-Amps, amplifiers, filters, A/D ● Interference

– Less of an issue

Page 11: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Coil 2

Coil 4

Coil 1

Coil 3

Multi-coilReconstruction

Page 12: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Multi-coilReconstruction

Page 13: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Multi-coilReconstruction

Recommended Reading: “The NMR Phase Array”, Roemer et al, MRM 1990

Page 14: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

IdealCoilSensitivity

Page 15: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Intheidealworld…

Page 16: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

SignalEquationwithCoils

Coil Sensitivity Modulation

Coil Sensitivity

Page 17: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

MRSignalEquation–DiscreteForm

1D Simplification

Discrete Form

Page 18: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

2-VoxelCase

A B

Page 19: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department
Page 20: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

4VoxelCase

A B C D

Page 21: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

InverseProblem

Orthonormal Fourier Encoding Matrix!

Page 22: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

4VoxelswithCoils

A B C DCoil 1 Coil 2

Page 23: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Over-determined!

Page 24: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Under-Sampling!

Sensitivity Encoding Matrix!

2X Acceleration

Page 25: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

k-spaceUnder-sampling

kx

ky

kx

ky

FFT➠

FFT➠

Page 26: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

SENSE

Image

Coil Sensitivity Information

Coil 2

Coil 1

Object

Unwrap fold over in image space

( )C rγ

!

Page 27: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

SensitivityEncodingMatrix

● A huge matrix! – 256*256*32 by 256*256

● Pseudo inverse can be simplified in Cartesian sampling

● For non-Cartesian scanning, conjugate gradient methods can be used to iteratively solve the inverse problem.

● Requires prior knowledge of coil sensitivity – Errors in coil sensitivity causes artifacts

Recommended Reading: “SENSE: sensitivity encoding for fast MRI”, Pruessmann et al, MRM 1999

Page 28: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Coiln

* =Undersampling

Object Object*Coiln Aliased

CartesianSENSE

Page 29: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Coiln

* =Undersampling

Object Object*Coiln Aliased

CartesianSENSE

* =

Undersampling

Page 30: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Coil 1

Page 31: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Coil 1 Coil 2

Page 32: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Coil 1 Coil 2 Coil 3 Coil N

Page 33: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

SENSERate-2

Known [n x 1]

Known [n x 2]

Unknown [2 x 1]

Page 34: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

SENSEandSNR

● R - reduction or acceleration factor – Loss associated with scan time reduction – Typically ~1/2 N-coils

● g - geometry factor – Loss associated with coil correlation – For R=1, g=1 – For R=2, g=~1.5-2

● SNR is spatially dependent – Higher in areas of aliasing

Page 35: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

HowFastCanWeGo?

Page 36: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

SensitivityEncodingMatrixConditioning

● Depends on several factors – Accuracy of coil sensitivity – K-space under-sampling pattern – Coil geometry and sensitivity

● Noise is amplified during inversion – G-factor

Page 37: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

ParallelImagingTradeoffs

Page 38: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

1/g-MapforRate-4

∞ elements 32 elements 16 elements

12 elements 8 elements

Relative SNR Scale

Page 39: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

G-factoranditsimpactonimage

Pruessmann et al, MRM 1999

Rate 1 2 2.4 3 4

g-m

apSE

NSE

alia

sed

Page 40: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

1/g-factormap&Rate-4

8-channel Head coil Rate-4 (tight FOV)

Page 41: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

OutstandingProblems

● SNR optimization – Coil design – Reconstruction algorithms

● Estimation of true coil sensitivities

Page 42: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

CoilSensitivityEstimation

Pruessmann et al, MRM 1999

Page 43: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Dependenceoncoilsensitivityaccuracy

Pruessmann et al, MRM 1999

● Images reconstructed using coil sensitivity maps calculated using different order P of polynomial fitting

P=0 P=1 P=2

Page 44: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

K-space based parallel imaging methods

Page 45: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Synthesizingspatialharmonics

IF

THEN

Page 46: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

UseofHarmonics:Skippingk-spacelines

kx

ky

Coil 1 Coil 2

n1 n 2

} Δky

Page 47: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Whatfrequencycanwesynthesize?

● Depends on the frequency component of coil sensitivities

● Extreme Example:

yCoi

l sen

sitiv

ity

C1(y) C2(y) Ccomp(y)

Page 48: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

SpatialHarmonics

Sodickson et al, MRM 38:591-603

Page 49: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

SMASH

ImageObjectCoil 2

Auto- Calibration

Coil 1

Reconstruct Missing k-space

Page 50: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Auto-CalibrationCoil 1 Coil 2

Page 51: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

VariationsofSMASH

Page 52: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Comparisonb/wSENSEandSMASH

● SMASH is a special case of SENSE – Spatial harmonics allow for reduction of

encoding matrix ● SMASH does not require direct measurement of

coil sensitivity – Auto-calibrating

● SENSE fails when FOV < Object size

Page 53: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

ParallelImagingSummary

● Parallel imaging uses coil sensitivities to speed up MRI acquisition

● Cases for parallel imaging – Higher patient throughput, real-time imaging,

imaging for interventions, motion suppression ● Cases against parallel imaging

– SNR starving applications, imaging coil map problems

Page 54: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

CompressedSensingMRI

● CS is a method complimentary to parallel imaging to speed up image acquisitions

● Two requirements – Sparsity in a transform domain – Random under-sampling

Page 55: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

● To the board…

Page 56: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

IntroductiontoCS

Lustig MRM 2007

Page 57: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

IntroductiontoCS

Lustig MRM 2007

Page 58: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

TypesofSparsity

● In image domain – CE-MR Angiography

● In temporal domain – cine cardiac MRI

● In both temporal and image domain – Dynamic CE-MRA – DCE perfusion

● …

Page 59: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

SparsityinMRAimages

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DCEMRAandPerfusion

● Background Subtraction before CS – Enhanced sparsity, higher temp. resol.

Storey, Lee, NYU, ISMRM 2010

Systole Diastole- = Diff.

Page 61: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Sparsity in Time

Page 62: Accelerated MRI Techniques: Basics of Parallel Imaging and ......Accelerated MRI Techniques: Basics of Parallel Imaging and Compressed Sensing Peng Hu, Ph.D. Associate Professor Department

Questions?● Peng Hu, Ph.D. ● 300 Medical Plaza B119 ● 310 267 6838 ● [email protected] ● http://mrrl.ucla.edu/meet-our-team/hu-lab/