sparse mri -

Michael (Miki) LustigDepartment of Electrical Engineering and Computer Science, UC Berkeley

“Randomness is too important to be left to chance.”*

*R. Conveyo, Oak Ridge National Laboratory

Sparse MRI

M. Lustig, EECS UC Berkeley

Rapid MRI

• MRI data collection is inherently slow

• Faster imaging would:– Decrease scan-time– Decrease image artifacts– Increase spatial/temporal

resolution– Increase coverage– Enable new applications

• Possible solution:– Faster imaging by reducing data

(exploiting correlations & redundancies)

ultrasound

x-ray

CT

Cardiovascularultrasound.com, siemensehealthcare.com, Jim Pipe, BNI

sub-Nyquist

• Redundancy reduces sampling requirements(The more you know, the less you need)

Nyquist limit


Data Redundancy

prior knowledge everything

Hennig limit

everything

nothing

mea

sure

men

ts

ParallelImaging

k-tBLAST

RIGRkeyhole

compressed sensing

HYPR


Towards the Henning Limit• There are situations where the Hennig limit is achievable. Yet,

somewhat not so informative

Prior knowledge saves scan time

Dr. I want a foot MRI!

This is going to bequick.....

Medical images are compressibleStandard approach: First collect, then compress


Image Compression

100110100110100010011101010100110100010001010110101010101011001011101110111010101011011011010100111111

1010001101001101011 Compression



Compressed Sensing

100110100110100010011101010100110100010001010110101010101011001011101110111010101011011011010100111111

1010001101001101011 Compression

Sensing



Compressed Sensing

100110100110100010011101010100110100010001010110101010101011001011101110111010101011011011010100111111

1010001101001101011 Compression

Sensing

*Courtesy, M. Uecker, J Frahm Max Planck

*


Example: DCE

delayed filling of aneurysm

J. Velkina and A. SamsonovUniversity of Wisconsin, Madison

Yijing Wu, Chuck MistrettaUniversity of Wisconsin, Madison

submilimiter spatial resolution~1 Frame/sec

CS-HYPR patient with dual arteriovenous fistula.

• Accelerated Cine Turbo-Spin-echo R=10


Example: Dynamic CINE

Courtesy, Denis Parker, University of Utah

2 Averages to avoid artifact Dynamic Cine

Mendes et al, MRM 66:1286, 2011


Example: 3D Real-time

• Real-time airway collapseR = 13

Mid-sagittal

Para-sagittal

Axial slicesSuperior

Inferior

Courtesy, YC Kim & K. Nayak, USC

normal breathing load during inspiration

Marked narrowing


A Surprising Experiment

recon

standard

sensing

Compressed

Randomly throw away84% of samples

Transform

Fourier

Candes, Romberg and Tao; 2004M. Lustig, EECS UC Berkeley

Implications…

Randomly throw away66% of samples

• MRI data are obtained in k-space

• Potential for significant scan time reduction

transform

Fourier

recon

standard

sensing

compressed


Compressed Sensing Hollywood Style

from: http://dunk3d.tumbler.com

•This software is state-of-the-art•With the right combination of algorithms...

•You got an image enhancer ?....

• x∈ℜN is a signal • Make N linear measurements


N N

Traditional Sensing

xy

=

Φ

sensing matrix

NxN

Desktop scanner/ digital camera sensing



N N

Traditional Sensing

xy

=

Φ

sensing matrix

NxN

MRI Fourier Imaging


N N

Traditional Sensing


xy

=

Φ

sensing matrix

NxN

A “good” sensing matrix is orthogonal

Φ* Φ = I

Arbitrary sensing


sensing matrix

Compressed Sensing (Candes, Romber, Tao 2006; Donoho 2006)

• x∈ℜN is a K-sparse signal (K<<N)• Make M (K<M<<N) incoherent linear projections

x

=

Φ

MxNK

sensing matrix

A “good” compressed sensing matrix is incoherent i.e, approximately orthogonal

Φ* Φ ≈ I

Incoherency can preserve information

M

y


CS recovery

• Given y = Φxfind x

• But there’s hope, x is sparse!

Under-determined

=

Φ xy


CS recovery

• Given y = Φxfind x

• But there’s hope, x is sparse!

minimize ||x||1

s.t. y = Φx

need M ≈ K log(N) <<N

Solved by linear-programming

Under-determinedminimum ||x||1 minimum ||x||2


Geometric Interpretation

domain of sparse signals


Practicality of CS

• Can such sensing system exist in practice?

Fourier matrix


Practicality of CS


Fourier matrix


Practicality of CS


Fourier matrix



• Randomly undersampled Fourier is incoherent

Φ* Φ ≈ I

Practicality of CS

=

• MRI samples in the Fourier domain!


S p a r s i t y &

Compressibility

not sparsesparse


Sparsity and Noise

*image courtesy of J. Trzasko

*


Sparsity and Noise

*image courtesy of J. Trzasko

sparse not sparse

*

denoise/separate by threshold


Transform Sparsity

not sparse Sparse Edges


Transform Sparsity and Denoising

sparsenot sparsewavelet transform

low-frequency

high frequency

denoised

DL Donoho, I Johnstone Biometrika 1994;81(3):425-55



sparsenot sparsewavelet transform

denoised

low-frequency

high frequency




wavelet denoising



More Sparse Transforms

time

posi

tion

posi

tion

temporal frequency

Sparse

not Sparse *Video courtesy of Juan Santos, Heart Vista

Courtesy, M. Usman & T. SchaeffterKing’s College

furtherexploit group

sparsity


Sparsity and Compression

• Only need to store non-zeros


http://xkcd.com/26/

From Sparse Signals to Sparse Sampling





uniform subsampling

coherentfolding



coherentfolding

uniform subsampling



random subsampling

non-coherentartifact



variable density random

noise-likeartifact



K. Scheffler, J. Hennig, MRM 1998; 40(3):474-80

undersampled radial

streakingartifact



D. Peters et. al, MRM 2000; 43:91-101

better resolution than the 4003 400 FT (512 with 1.3 largerFOV). This places a lower limit on the actual resolution ofundersampled PR in this imaging situation.

Human StudiesThis section presents the results from four contrast-enhanced exams, out of the 10 exams conducted using PRwith contrast agent in healthy volunteers and a patient.

ZIPR With Progressively Fewer ProjectionsFigure 7 shows the femoral arteries imaged with ZIPRduring contrast agent infusion, originally collected as a 512(312 acquired) 3 400 projection angle PR image using thefollowing parameters: 40 3 40 3 11.2 cm FOV, 30° tip,TR/TE of 8.0 ms/1.1 ms, 664 kHz BW, 312 3 400 projec-tions3 16 kz3 1 frame acquisition matrix, 5123 5123 16reconstruction matrix, 0.78 3 0.78 3 7.0 mm true voxelsize, 51 s scan time, 0.3 mmol/kg at 0.5 ml/s gadoliniumcontrast agent injection, and torso phased array coil.Images were reconstructed with progressively fewer angles(using (a) 400, (b) 200, (c) 100, and (d) 50 angles) byskipping angles in the full dataset. The changing imagequality is due to the worsening of artifacts and reduction ofSNR at lower numbers of projections. Nevertheless, clini-

FIG. 6. Quantitative resolution comparison between FT and PR inthe resolution phantom for FT acquisitions with 512 phase encodings,400 phase encodings, 128 phase encodings, and PR with 128projections. The magnitude of oscillations for each dot pattern isrecorded. The 128 PR method performs similarly to the 512 FTmethod, and better than the 400 FT method.

a b cFIG. 5. Resolution comparison between FT and PR. a: FT 5123 128 phase encodings. b: PR 5123 128 projections. c: FT 5123 512 phaseencodings. The pixel resolution of the 512 3 512 image is 0.3 3 0.3 mm, and the smallest dots are 0.5 mm wide, spaced 0.5 mm apart. Theundersampled PR image has resolution similar to the 512 3 512 FT image, although it was acquired in one-fourth of the time. The Fourierfrequency-encoding direction is indicated by the arrow.

Undersampled PR for MRA 95

cally significant detail is present, even with 50 projections(an undersampling factor of 16 relative to fully sampledPR).

ZIPR Comparisons Between FT and PR in HumansTo evaluate undersampled PR for contrast-enhanced MRA,3D volumes obtained using the FT and PR imaging meth-ods were compared in a contrast-enhanced scan of thepulmonary vessels. MIP comparisons between FT (512 3128 phase encodings) and PR (512 3 128 projections) arepresented in Fig. 8. The following parameters were used:36 3 36 3 12.8 cm FOV, 30° tip, TR/TE 7.5 ms/1.2 ms,664 kHz BW, 312 3 128 projections or phase encodings 332 kz 3 1 frame acquisition matrix, 512 3 512 3 64reconstruction matrix, 0.70 3 0.70 3 4 mm true voxel sizefor PR, 0.7 3 2.8 3 4 mm true voxel size for FT, 31 s scantime, 18 ml at 1 ml/s gadolinium contrast agent injection,and a torso phased array coil. Minimal undersamplingartifact is visible in the PR images. The comparison clearlyillustrates significant improvement in resolution for PR inthe Fourier phase encoding (horizontal) direction. The FT

MIPs show better SNR and more vessels. The PR imageshave sharper vessels.

Fast Pulmonary ImagingOne use of undersampled PR is for fast moderate-resolution imaging. For example, patients with suspectedpulmonary embolism can only tolerate short breathholds.In Fig. 9 we compare contrast-enhanced FT and PR

pulmonary angiograms both obtained in a 17-sec breath-hold. We compare targeted MIPs of the undersampled PRand FT. The scan parameters for PRwere: 363 363 9.6 cmFOV, 40° tip, TR/TE 5 6.0 ms/1.2 ms, 664 kHz BW, 400(240 acquired) 3 170 projections 3 16 kz, 512 3 512 3 32reconstruction matrix, true voxel size 0.9 3 0.9 3 6 mm,27 mls at 2 ml/s gadolinium contrast agent injection, fatsuppression pulse once per slice loop, and a cardiacphased array coil. For the FT scan (Fig. 9b), all parameterswere the same except 256 xres (160 acquired) and a 128phase encodings resulting in 1.43 2.83 6.0 mm true voxelsize. The comparison shows the much better resolution of

a

c

b

dFIG. 7. ZIPR MIPs of the femoral arteries, all generated from the same data set using progressively fewer number of projections: (a) 400, (b)200, (c) 100, (d) 50. Even with 50 projections (d), clinically significant detail is present. The origin of the profunda femoral artery at the commonfemoral artery is well depicted.

96 Peters et al.

undersampled radial

• For sparse signals - artifacts are benign• Excellent for angiography• Often MIP through volume (like thresholding)


Compressed Sensing “denoising” artifacts


• Take compressible signals Have sparse transform representations

• Make incoherent measurements Make artifacts look like noise (after transform)

• Reconstruct using sparsity-enforcing non-linear reconstructionIteratively separate sparse signals from artifacts

Compressed Sensing - Basic Idea

Ingredients:


Intuitive Example of Compressed Sensing



iFFT

Nyquistsampling



iFFT

sub-Nyquistequispaced



iFFT

sub-Nyquist

Ambiguity



iFFT

sub-Nyquistrandom



iFFT

sub-NyquistLooks like

“random noise”



iFFT

sub-NyquistBut it’s not

noise!


Intuitive example of CS

iFFT

Recovery

Example inspired by Donoho et. Al, 2007


Question!

• What if the signal is sparse, and we sample it directly?

• Would CS still work?

sub-Nyquistrandom sub-Nyquist


Answer...

• What if the signal is sparse, and we sample it directly?

• Would CS still work?

sub-Nyquistrandom sub-Nyquist

Most likely we will get only zeros!M. Lustig, EECS UC Berkeley

Domains in Compressed Sensing

Signal

SparseDomain

SamplingDomain

Not Sparse!

Sparse! incoherent


Domains in CS MRI

Signal

k-space

Wavelet domain incoherent

Signal domain


Domains in CS MRI

x-f domain incoherent

k-t domainx-t domain

Acquired Data

Sparse “denoising”

Compressed SensingReconstruction

Acquired Data

Sparse “denoising”


Acquired Data

Sparse “denoising”Undersampled Final Image


Tutorial & code available at http://www.mlustig.comM. Lustig, EECS UC Berkeley

Practical Considerations

The theory can only take you so far... • Many practical considerations

– Weak sparsity of medical images

– Noise

– Sampling (pure random infeasible!)

– System imperfection

– Complex numbers / phase

– Parallel imaging

– Computation

– Validation?

– ......

• Noise– Noise in the sparse domain counts!– Subsampling reduces SNR– Resulting image noise is not white-Gaussian– Apparent SNR ≠ Sensitivityonly use when SNR is sufficient!


Limitations and Pitfalls

remainingartifact “noise” True noise


Artifacts

Blurred Blocky Good quality

• Artifacts: ( when pushed to limits)

• Usually easy to recognize• Can be subtle

– Washed contrast

– Loss of resolution

– Synthetic/artificial look

– Blocky artifacts

Example courtesy M. Uecker, UCB


Trade-offs

• CS provides new tradeoffs– Loss of low-contrast

features instead of resolution

acce

lera

tion

Low-Resolution Compressed Sensing


Incoherent sampling3D “Full” 3D “Compressed”


Incoherent Sampling

t

kyy

kx

2D non-Cartesian3D Cartesian

k-t sampling

Lustig et. al, MRM 2007;58(6):1182-95Santos et. al, MRM 2006;55:371-9Doneva et. al, ISMRM 2011Block KT, et. al, MRM 2007;57:1086-98Haider C. MRM 2008;60:749-760Graiser et. al, MRM 2003;50:1266-75


Compressed Sensing Meets

Parallel Imaging


Coil Arrays


Parallel Imaging and Compressed Sensing

• Synergetic combination• Used to

– Increase speed– Improve quality

• SENSE based methods• Auto-Calibrating methods

Block, et. al, MRM 2007;57:1086-1098

Wu et. al, ISMRM’08 pp.1480King et. al, ISMRM’08 pp. 1488Liu, Ying et. al, ISMRM’08 pp. 3154Otazo et. al, MRM 2010;64:767-76

Lustig et. al, MRM 2010;64:457-71

Liang, Ying et. al, MRM 2009;62:1574-84


SENSE Parallel Imaging and CS

1030 Trzasko et al.

FIG. 7. Selected images from Example 5: (a–c) are coronal MIPs of early, middle, and late filling stage volumes from a nonview-sharedSENSE + Homodyne reconstruction of the calves of a volunteer, and (d) is an axial cross-section of a middle filling stage volume; (e–g) and(h) are from the corresponding NCCS reconstruction. The location of the axial cross-section is marked by the dotted line in (b) and (f). (i) and(j) are the respective enlargements of an ROI in (b) and (f); (k) and (l) are the respective enlargements of an ROI in (d) and (h).

Another limitation of the proposed reconstruction strat-egy is that both the recovery model and the numericaloptimization routine each possess several parameters thatmust be reasonably assigned to achieve high quality results.For example, assigning too small a value to the regulariza-tion parameter, α, can allow noise amplification during thereconstruction, whereas assigning too large a value to α canresult in over-sparsification and thus over-smoothing of theimage, and a corresponding loss of features. However, it isnoted that once an effective setting is found for a particu-lar image scenario, it can be reused (e.g., all neurovascularstudies are run under the same settings).

Although beyond the scope of this manuscript, it isexpected that the improved vessel-to-background con-spicuity (i.e., contrast) and homogeneity of vessels, enhanc-ing structures, and background tissue resulting from theNCCS reconstruction strategy for CAPR CE-MRA imageseries will lead to improved diagnosis, with better sen-sitivity for detection of abnormalities, and fewer falsepositive/negative interpretations. Nonetheless, a formalradiological comparison of these two reconstruction strate-gies is still needed and will be the subject of a separate,future work.

APPENDIX: FINITE SPATIAL DIFFERENCECOMPUTATION

The adopted finite difference spatial model assumes thatany finite spatial difference centered inside Ω but for whichthe neighbor of interest is outside Ω will be zero. Morespecifically, ∀s ∈ Ω and any n,

[Dnu](s) =

u(s) − u(s + n), if (s + n) ∈ Ω

0, else .

Note that this operator can be abstracted as Dn = I −Sn−Cn,where I is the identity operator, Sn is a non-wrapped shiftoperator (towards neighbor n) with zero-filling, and Cn isan operator that copies nonshifted boundary elements. Letn = ∆x , ∆y , ∆z and s = x, y , z, where x ∈ [0, Nx ), y ∈[0, Ny ), and z ∈ [0, Nz). Assuming the notation u(s + n) =u(x + ∆x , y + ∆y , z + ∆z), the component operators of Dncan then be defined as

[Snu](s) =

u(s + n), if (x ∈ Υx ) ∧ (y ∈ Υy ) ∧ (z ∈ Υz)0, else

[20]

1030 Trzasko et al.

FIG. 7. Selected images from Example 5: (a–c) are coronal MIPs of early, middle, and late filling stage volumes from a nonview-sharedSENSE + Homodyne reconstruction of the calves of a volunteer, and (d) is an axial cross-section of a middle filling stage volume; (e–g) and(h) are from the corresponding NCCS reconstruction. The location of the axial cross-section is marked by the dotted line in (b) and (f). (i) and(j) are the respective enlargements of an ROI in (b) and (f); (k) and (l) are the respective enlargements of an ROI in (d) and (h).

Another limitation of the proposed reconstruction strat-egy is that both the recovery model and the numericaloptimization routine each possess several parameters thatmust be reasonably assigned to achieve high quality results.For example, assigning too small a value to the regulariza-tion parameter, α, can allow noise amplification during thereconstruction, whereas assigning too large a value to α canresult in over-sparsification and thus over-smoothing of theimage, and a corresponding loss of features. However, it isnoted that once an effective setting is found for a particu-lar image scenario, it can be reused (e.g., all neurovascularstudies are run under the same settings).

Although beyond the scope of this manuscript, it isexpected that the improved vessel-to-background con-spicuity (i.e., contrast) and homogeneity of vessels, enhanc-ing structures, and background tissue resulting from theNCCS reconstruction strategy for CAPR CE-MRA imageseries will lead to improved diagnosis, with better sen-sitivity for detection of abnormalities, and fewer falsepositive/negative interpretations. Nonetheless, a formalradiological comparison of these two reconstruction strate-gies is still needed and will be the subject of a separate,future work.

APPENDIX: FINITE SPATIAL DIFFERENCECOMPUTATION

The adopted finite difference spatial model assumes thatany finite spatial difference centered inside Ω but for whichthe neighbor of interest is outside Ω will be zero. Morespecifically, ∀s ∈ Ω and any n,

[Dnu](s) =

u(s) − u(s + n), if (s + n) ∈ Ω

0, else .

Note that this operator can be abstracted as Dn = I −Sn−Cn,where I is the identity operator, Sn is a non-wrapped shiftoperator (towards neighbor n) with zero-filling, and Cn isan operator that copies nonshifted boundary elements. Letn = ∆x , ∆y , ∆z and s = x, y , z, where x ∈ [0, Nx ), y ∈[0, Ny ), and z ∈ [0, Nz). Assuming the notation u(s + n) =u(x + ∆x , y + ∆y , z + ∆z), the component operators of Dncan then be defined as

[Snu](s) =

u(s + n), if (x ∈ Υx ) ∧ (y ∈ Υy ) ∧ (z ∈ Υz)0, else

[20]

JD Trzasko et. al, Mayo ClinicMRM 2011;66:1019-32

R = 8

SENSE CS+SENSE

raw slices raw slices

Cartesian 3D PR (CAPR)1020 Trzasko et al.

FIG. 1. An example W = 4 CAPR acquisition sequence (Ny = Nz = 256). During this acquisition, the phase-encoded plane of k-space(ky-kz) is partitioned into a distinct low-pass region, shown in orange, and a high-pass region (a). The high-pass annulus is itself furtherpartitioned azimuthally into W subsets of “vanes,” shown here in blue, green, yellow, and red, which are placed asymmetrically aboutthe origin. Although Cartesian, the CAPR sampling operator, by construction, tends to exhibit properties similar to non-Cartesian radialtrajectories (within the phase-encoded plane). The sampling order or schedule is shown in (b). During each temporal update, uniformly-spaced samples (here, spaced 2 × 2 apart) from within the low-pass region and a single high-pass vane set are acquired. This same set ofk-space indices is reinvestigated after W temporal updates. The set of all k-space indices investigated at any point during the entire exam isshown in (c) and is simply the union of the sample sets shown in (b). Note that, for this example, only about 20% of k-space is investigatedduring the exam, a property that facilitates practical formation of the reference signal needed for background subtraction.

THEORY

A Forward Model for Parallel MRI

Suppose we are interested in forming a discrete image esti-mate of some anatomy of interest using three-dimensionalCartesian (3DFT) parallel magnetic resonance imaging.Denoting f as the discrete image of interest, a commonly-assumed forward model for this acquisition process is

g1g2...

gC

=

ΦFΓ1ΦFΓ2

...ΦFΓC

f + n, [1]

where gc is the signal observed by the cth coil sensor, Γcis the element-wise (i.e., diagonal) spatial sensitivity func-tion for the cth coil sensor, F is the discrete 3D Fouriertransform (3DFT) operator, and Φ is a binary operator thatidentifies the subset of k-space measured during the imag-ing experiment. The vector n represents system noise and ishereafter assumed to be a complex additive white Gaussianprocess (13).

Time-Varying Signals and CAPR

In CE-MRA, the signal of interest is inherently tran-sient and thus routinely probed at multiple different timepoints to characterize patient hemodynamics in addi-tion to vascular morphology. Given the direct relationshipbetween the number of k-space indices measured duringan MRI exam and the duration of the exam, spatiotemporalundersampling is often employed to accelerate dynamic

MRI exams such as CE-MRA. Reconstruction techniquessuch as view-sharing (25), HYPR-type processing (8,26),and constraint or regularization methods (9,23,27–33) thatrely on a priori assumptions about spatial and/or temporalimage structure may be employed to avoid generation ofimages with significant artifacts.

Assuming that both the signal of interest and the sam-pling process may be temporally variant in dynamic MRI,(1) can be generalized to

g1(t)g2(t)

...gC (t)

=

Φ(t)FΓ1Φ(t)FΓ2

...Φ(t)FΓC

f (t) + n(t), [2]

where t ≥ 0 is an integer corresponding to the frame num-ber. During a CAPR acquisition, k-space is partitioned intotwo distinct regions: (1) a circularly-symmetric low-passregion that is sampled during each temporal update; (2)a high-pass region of which a different subset is sampledduring each temporal update. Thus, the effective samplingoperator for CAPR can be described as

Φ(t) =[

ΦLOΦHI(t)

]. [3]

The dynamic high-pass sampling operator ΦHI(t) is alsostrictly W -periodic and so, ∀t ≥ 0, ΦHI(t) = ΦHI(t+W ), and∀τ ∈ (0, W ), Trace(Φ*

HI(t+τ)ΦHI(t)) = 0. A pictorial exampleof a CAPR acquisition sequence is given in Fig. 1. For a moredetailed description of the CAPR acquisition protocol, thereader is referred to (11).


SENSE Parallel Imaging and CS

• 8-fold acceleration• 10 slices per heartbeat• Temporal resolution = 60ms/slice• Spatial resolution (in-plane) = 1.7 mm• SENSE +PI

Perfusion images(peak myocardial wall enhancement)

Delayed-enhancement

Otazo et al. NYUMagn Reson Med. 2010; 64:767-76

Patient with acute myocardial infarction

First-Pass perfusion MRI

t

kyy

kx


AutoCalibrating Parallel Imaging and CSL1-SPIRiT CS+PI6 years oldR = 83D SPGR0.87x0.87x1.6 mm

Vasanawala & Alley, LPCH, StanfordM. Lustig et. al, UCB

MIP

slice

L1-SPIRiT

temporal phases


AutoCalibrating Parallel Imaging and CS

6 years old maleR = 83D SPGRSub-mm32 channels

L1-SPIRiTPI + CS

autocalibratingParallel Imaging

Vasanawala & Alley, LPCH, StanfordM. Lustig et. al, UCB


Compressed Sensing in the Clinic

• Target: Robust, sedation-free pediatric body MRI

• Leverage:dedicated 32ch coilCompressed SensingMotion CorrectionParallel Computing

• ~6 clinical scan / day at LPCHsince 2010

dedicated 32Ch coil

GPU’s & multi-core CPU

Berkeley Stanford GE


Reconstruction speed

• Iterative reconstruction computationally intensive• Large data-sets are better for CS • Currently top hurdle in penetration to clinic• Current Solutions:

– Algorithmic – Parallel Computation

D. Kim, J. Trzasko, A. Manduca et. al “High Performance 3D CS MRI Reconstruction Using Many-Core Architectures, IJBI doi:10.1155/2011/473123Intel and Mayo Clinic

1-3min for 3D datasets

M. Murphy, M. Lustig et. al, “Fast L1-SPIRiT CS PI MRI:Parallel Implementation and Clinically Feasible Scan-Time” IEEE-TMI 2012; early viewUC Berkeley, Stanford University


Emerging Techniquesand Applications


Multi-Contrast Reconstruction• An exam consists of multiple scans• Mutual information between exams• Jointly reconstruct all exams

joint reconseparate recon*B. Bilgic et. al, MIT MRM 2011;66:1601-15,

err.

x10

R=2.

4

T1w

T2w

+F. Huang, ISMRM ’12 pp2539 Philips

R=5

err.

x5


Compressive Parameter Mapping (T1,T2)CS#&#PI#(R=

6)GR

APPA

#(R=4)

TE#=#10#ms T2#map#R=#6

0

80#ms

J. Chul Ye - k-t FOCUSS KaistFeng L et al. Magn Reson Med. 2011; 65(6): 1661-9

Doneva et al Magn Reson Med 2010, 1114-1120Philips Research

Time

T1 map R = 8

T2#relaxa=on

• Preclinical models of cancer• CS for high-res + dynamics


Metabolic Imaging Hyperpolarized 13C

R = 7.5

Hu, Vigneron et. al, JMR 2008;192(2):258Hu, Vigneron et. al, MRM 2010;63(2):312P. Larson, et. al, MRM 2011;65(3):3:610-9UCSF

Regular

Compressedsensing

R = 18

Tumor

pyruvate lactate

• Transform can be adapted• Better sparsity/model = better recon


k-SVD Transform

S. Ravishankar and Y. Br

Adaptive Transforms Dabov et al, IEEE TIP, 2007.M. Aharon,et al, IEEE TSP 2006;54(11):4311-22

Block-Matching 3D


Adaptive Compressed Sensing

LOST: High-res

Late Gadolinium Enhancement R=3

2D Random Sampling - 6 fold undersampling

0

0.05

0.1

0.15

0.2

0.25

0.3

LDP reconstruction (22 dB) LDP error magnitude

0

0.05

0.1

0.15

0.2

0.25

0.3

DLMRI reconstruction (32 dB) DLMRI error magnitude

S. Ravishankar and Y. Bresler DLMRI


0

0.05

0.1

0.15

0.2

0.25

0.3


0

0.05

0.1

0.15

0.2

0.25

0.3




0

0.05

0.1

0.15

0.2

0.25

0.3


0

0.05

0.1

0.15

0.2

0.25

0.3




0

0.05

0.1

0.15

0.2

0.25

0.3


0

0.05

0.1

0.15

0.2

0.25

0.3



Fixed xForm (Wavelet)

DictionaryLearning*

*S. Ravishankar and Y. Bresler, UIUCIEEE TMI 2011;30(5):1028-41

non-Accelerated Dictionary Learning R=6

M. Akçakaya, R. Nezafat et. al Harvard/Beth IsraelMRM 2011;66(3):756-67

1.3x1.3x1.3mm31.7x1.7x4mm3

47-year old male patient undergoing CABG


Low-Rank Matrix CompletionR = 24

sparseSENSE + low rank R=6

sparse+lowrank sliding window

sparseSENSE Low-rank model R = 5

Courtesy:Zhi-Pei Liang, UIUCR. Otazo, NYUJ. Trzasko, Mayo Clinic


Conclusion & Comments

• Compressed Sensing: Sparsity, Incoherency and NL-recon

• Implementation must adapt to application• Use when limited by encoding time, not SNR• Larger dimensions are better

– 3D, dynamic, flow, diffusion....


What about fMRI?

• Sampling– EPI not ideal for CS

• Representation– what’s a good model for fMRI signal?

• My take:– CS in fMRI is possible and can be advantageous– But, no single silver bullet solution– Must tailor for experiment, task


Personal Note

• Take IT EASY! Acceleration costs!– Use carefully and responsibly

• CS has matured, but still missing clinical validation and clinical experience

• Share your code and work so it can be reproduced

http://www.eecs.berkeley.edu/~mlustig/Software.html


AcknowledgmentsSLIDES:

• Brian Hargreaves, Stanford

• Pauline Worters, Stanford

• Shreyas Vasanawala, Stanford

• Yoram Bresler, UIUC

• Zhi-Pei Liang, UIUC

• Denis Parker, Uni. of Utah

• Leslie Ying, Buffalo

• Reza Nezafat , BIDMC

• M. Akçakaya

• Feng Huang, Phillips

• Mariya Doneva, Phillips

• Anita Flynn, Berkeley

• Tobias Schaeffter, King’s College

• Muhammad Usman, king’s College

• Daniel Vigneron, Peder Larson, UCSF

• Jonh Chul-Ye, Kaist

• Berkin Bilgic, Elfar Adalsteinsson, MIT

• Maxim Zaitsev, Freiburg

• Martin Uecker, Max Planck & Berkeley

• Luca Marinelli, GE global research

• Ricardo Otazo, NYU

• Chuck Mistretta, Yijing Wu, UW

• Julia Velikina, Alexey Samsonov, UWNIH R01-EB009690, RR09794-15

GE Healthcare

Morgridge Foundation

American Heart Association

UC Discovery

“Everything to do with compression is very contentious in medical imaging. Every time you throw bits away somebody gets very nervous about it. The fortunate thing about ....[compressed sensing]... is that you don’t collect them in the first place, and that’s a much better situation!”

John Pauly 2007

Thank Youתודה רבה

http://www.eecs.berkeley.edu/~mlustig

sparse mri -

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