Parallel Imaging Reconstruction Multiple coils - “parallel imaging” Reduced acquisition times. Higher resolution. Shorter echo train lengths (EPI). Artefact reduction. Multiple coils have previously been used for SNR improvements, reduced acquisition times, and the rejection and replacement of isolated, motion-corrupted k-space lines. This work aims to use a fully sampled k-space and the ability of SMASH-based methods to predict k-space, to detect and correct motion corrupted data.

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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

Merits of collecting sensitivity data Pre-scan In data 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.

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.

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

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

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.

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?)