1. Compressed Sensing for Motion Artifact Reduction # 4593 Joëlle K. Barral & Dwight G. Nishimura Presentation: Wednesday @ 3pm Electrical Engineering Stanford University

2. Compressed Sensing for Motion Artifact Reduction# 4593 2 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:

3. Compressed Sensing for Motion Artifact Reduction# 4593 3 Motion Artifacts Blurring 78x156x500 μ m 3 11 min 02 s CALF SKIN Ghosting 391x521x1000 μ m 3 2 min 04 s LARYNX

4. Compressed Sensing for Motion Artifact Reduction# 4593 4 Ehman MRI 1989:173:255-263 -- Wang MRM 1996:36:117-123 -- Song MRM 1999:41:947-953 Zero-padding FFT Cross-correlation Shifts Fast Large Angle Spin Echo 3D FLASE TR = 80 ms kx ky kz Phase-modulation Projections Projection along x TR number 64 512 64 kx Navigators interleaved Classical Navigators

5. Compressed Sensing for Motion Artifact Reduction# 4593 5 Rejecting Outliers 2% outliers 256x12 encodes LARYNX -- Volunteer scan Shift of small amplitude, well approximated by a translation Shift of large amplitude, that cannot be corrected = outlier kzkz kyky Resulting undersampled trajectory after outliers rejection: SI: Superior/Inferior AP: Anterior/Posterior LR: Left/Right

6. Compressed Sensing for Motion Artifact Reduction# 4593 6 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

7. Compressed Sensing for Motion Artifact Reduction# 4593 7 256x32 encodes, 30% outliers Simulation with in-vivo data 3DFT CS Sequential acquisitionPseudo-random acquisition Compressed Sensing (1/2)

8. Compressed Sensing for Motion Artifact Reduction# 4593 8 POCS Compressed Sensing (2/2) Haacke JMR 1991:92:126-145 -- Lustig MRM 2007:58:1182-1195 256x32 encodes, 30% outliers 3DFTCS

9. Compressed Sensing for Motion Artifact Reduction# 4593 9 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?

10. Compressed Sensing for Motion Artifact Reduction# 4593 10 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

11. Compressed Sensing for Motion Artifact Reduction# 4593 11 Coherency Determine prioritized list of encodes to reacquire 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

12. Compressed Sensing for Motion Artifact Reduction# 4593 12 Conclusion Undersampled trajectory ✦ Diminishing Coherency Algorithm Incoherent undersampled trajectory ✦ Pseudo-random acquisition ✦ Outliers rejection

13. Compressed Sensing for Motion Artifact Reduction# 4593 13 Thank you! Contact: jbarral@stanford.edu Acknowledgments: Michael Lustig, Bob Schaffer, Uygar Sümbül, Juan Santos