Parallel Imaging Reconstruction

1. Parallel Imaging Reconstruction • Reduced acquisition times. • Higher resolution. • Shorter echo train lengths (EPI). • Artefact reduction. Multiple coils - “parallel imaging”

2. K-space from multiple coils coil views coil sensitivities multiple receiver coils k-space simultaneous or “parallel” acquisition

3. Undersampled k-space gives aliased images SAMPLED k-space k-space Fourier transform of undersampled k-space. coil 1 FOV/2 coil 2 Dk = 2/FOV Dk = 1/FOV

4. SENSE reconstruction ra p1 coil 1 rb coil 2 p2 Solve for ra and rb. Repeat for every pixel pair.

5. Image and k-space domains object coil sensitivity coil view Image Domain multiplication x = s c r FT k-space convolution = R C S coil k-space “footprint” object k-space

6. Generalized SMASH image domain product k-space convolution matrix multiplication = R S C gSMASH1 matrix solution 1Bydder et al. MRM 2002;47:16-170.

7. Composition of matrix S Acquired k-space coil 1 coil 2 hybrid-space data column S FTFE process column by column

8. Coil convolution matrix C C FTPE coil sensitivities hybrid space cyclic permutations of &

9. missing samples (can be irregular) gSMASH coil 1 = coil 2 S R C requires matrix inversion

10. Linear operations • Linear algebra. • Fourier transform also a linear operation. • gSMASH ~ SENSE • Original SMASH uses linear combinations of data.

11. SMASH - + - + + + + + PE weighted coil profiles sum of weighted profiles Idealised k-space of summed profiles 1st harmonic 0th harmonic

12. SMASH data summed with 0th harmonic weights = R data summed with 1st harmonic weights easy matrix inversion

13. GRAPPA • Linear combination; fit to a small amount of in-scan reference data. • Matrix viewpoint: • C has a diagonal band. • solve for R for each coil. • combine coil images.

14. Linear Algebra techniques available • Least squares sense solutions – robust against noise for overdetermined systems. • Noise regularization possible. • SVD truncation. • Weighted least squares. Absolute Coil Sensitivities not known.

15. Coil Sensitivities • All methods require information about coil spatial sensitivities. • pre-scan (SMASH, gSMASH, SENSE, …) • extracted from data (mSENSE, GRAPPA, …)

16. One-off extra scan. Large 3D FOV. Subsequent scans run at max speed-up. High SNR. Susceptibility or motion changes. No extra scans. Reference and image slice planes aligned. Lengthens every scan. Potential wrap problems in oblique scans. Merits of collecting sensitivity data Pre-scan In data

17. PPI reconstruction is weighted by coil normalisation coil data used (ratio of two images) reconstructed object • c load dependent, no absolute measure. • N root-sum-of-squares or body coil image.

18. Handling Difficult Regions body coil raw (array/body) array coil image thresholded raw local polynomial fit filtered threshold region grow www.mr.ethz.ch/sense/sense_method.html

19. ra p1 rb p2 SENSE in difficult regions coil 1 coil 2

20. Sources of Noise and Artefacts • Incorrect coil data due to: • holes in object (noise over noise). • distortion (susceptibility). • motion of coils relative to object. • manufacturer processing of data. • FOV too small in reference data. • Coils too similar in phase encode (speed-up) direction. • g-factor noise.

21. Tips • Reference data: • avoid aliasing (caution if based on oblique data). • use low resolution (jumps holes, broadens edges). • use high SNR, contrast can differ from main scan. • Number of coils in phase encode direction >> speed-up factor. • Coils should be spatially different. • (Don’t worry about regularisation?)