Parallel Imaging Reconstruction Multiple coils parallel imaging Reduced

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

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

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

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

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

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

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

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

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

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

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

SMASH data summed with 0 th harmonic weights = R data summed with 1 st 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, g. SMASH, SENSE, …) – extracted from data (m. SENSE, GRAPPA, …)

Merits of collecting sensitivity data Pre-scan • One-off extra scan. • Large 3 D FOV. • Subsequent scans run at max speed-up. • High SNR. • Susceptibility or motion changes. In data • 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_method. html

SENSE in difficult regions ra p 1 coil 1 rb coil 2 p 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? )