Compressed Sensing for Motion Artifact

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Joëlle K. Barral & Dwight G. Nishimura

Presentation: Wednesday @ 3pm

Electrical Engineering Stanford University

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In a Nutshell

a Compressed Sensing approach can be used to reduce motion artifacts in high-resolution MRI.

Navigators are useful to correct motion of small amplitude.

They can also be used to detect data that needs to be discarded.

Discarding data provides an undersampling dataset:

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Motion Artifacts

Blurring

78x156x500 μm3

11 min 02 s

CALF SKINGhosting

391x521x1000 μm3

2 min 04 s

LARYNX

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Ehman MRI 1989:173:255-263 -- Wang MRM 1996:36:117-123 -- Song MRM 1999:41:947-953

Zero-Zero-padding padding

FFTFFT

Cross-Cross-correlationcorrelation

ShiftShiftss

Fast Large Angle Spin Echo

3D FLASE

TR = 80 ms

kx ky kz

Phase-Phase-modulationmodulation

ProjectioProjectionsns

Projection along x

TR number

64512 64 kx

Navigators interleaved

Classical Navigators

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Rejecting Outliers

2% outliers256x12 encodes

LARYNX -- Volunteer scan

Shift of small amplitude, well approximated by a translation

Shift of large amplitude, that cannot be corrected= outlier

kz

ky

Resulting undersampled trajectory after outliers rejection:

SI: Superior/InferiorAP: Anterior/PosteriorLR: Left/Right

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Randomizing the Acquisition

Korin JMRI 1992:2:687-693 -- Wilman MRM 1997:38:793-802 -- Bernstein MRM 2003:50:802-812

256x16 encodes, 11% outliers

Sequential acquisitionPseudo-random acquisition

Phantom scans -- FLASE sequence

"A man has made all his decisions at random. He did not do worse than others who consider carefully their choices" Paul Valéry

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256x32 encodes, 30% outliers

Simulation with in-vivo data

3DFT

CSCS

Sequential acquisitionPseudo-random acquisition

Compressed Sensing (1/2)

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POCS

Compressed Sensing (2/2)

Haacke JMR 1991:92:126-145 -- Lustig MRM 2007:58:1182-1195

256x32 encodes, 30% outliers

3DFT CS

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Discussion

A pseudo-random acquisition often avoids getting corrupted samples that are contiguous in k-space.

If the undersampled trajectory (after outlier rejection) is incoherent, Compressed Sensing allows an accurate reconstruction.

However, how can the acquisition be robust against the worst case scenario (since motion is truly random) where the undersampled trajectory that we first get is not incoherent?

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Diminishing Variance Algorithm

Acquire encodes and navigators

Compute shifts

Determine prioritized list of encodes to

reacquire

Outliers

Sachs MRM 1995:34:412-422

Priority = distance from histogram mode

(weighted by distance from k-space origin)

Number of pixels

mm

mode

Scan time:

6 min 12 s

(38 s overhead to

reacquire the outliers)

Scan time:

5 min 34 s

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Coherency

Determine prioritized Determine prioritized list of encodes to list of encodes to

reacquirereacquire

Acquire encodes and navigators

Compute shifts

Determine prioritized list of encodes to

reacquire

pseudo-

randomly

Priority = incoherency of the underlying undersampled

trajectory

Future work: Diminishing Variance Algorithm

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Conclusion

Undersampled trajectory

Diminishing Coherency AlgorithmIncoherent undersampled

trajectory

Pseudo-random acquisition

Outliers rejection

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Thank you!

Contact:

jbarral@stanford.edu

Acknowledgments:

Michael Lustig, Bob Schaffer, Uygar Sümbül, Juan Santos