Parallel Imaging Reconstruction

• Reduced acquisition times.

• Higher resolution.

• Shorter echo train lengths (EPI).

• Artefact reduction.

Multiple coils - “parallel imaging”

k-space

coilviews

coilsensitivities

multiplereceiver coils

simultaneous or “parallel” acquisition

K-space from multiple coils

k-space SAMPLEDk-space Fourier transform

of undersampledk-space.

k = 2/FOV

FOV/2

k = 1/FOV

Undersampled k-space gives aliased images

coil 1

coil 2

SENSE reconstruction

coil 1

ra

rb

coil 2p2

p1

Solve for ra and rb.Repeat for every pixel pair.

2/)( ,1,11 bbaa rcrcp

2/)( ,2,22 bbaa rcrcp

=x

object coil sensitivity coil view

=

object k-space coil k-space“footprint”

FT

Image Domainmultiplication

k-space convolution

scr

R C S

Image and k-space domains

Generalized SMASH

crs

RCS

image domain product

k-space convolution

matrix multiplication

SCR \1 SC gSMASH1 matrix solution

1 Bydder et al. MRM 2002;47:16-170.

=S C R

Composition of matrix S

FTFE

process column by column

Shybrid-spacedata column

Acquired k-space

coil 1

coil 2

Coil convolution matrix C

Chybridspace

cyclic permutations of &

coilsensitivities

FTPE

gSMASH

=

S C R

missing samples(can be irregular)

SCR \requires matrix inversion

coil 1

coil 2

Linear operations

• Linear algebra.

• Fourier transform also a linear operation.

• gSMASH ~ SENSE

• Original SMASH uses linear combinations of data.

SMASH

+ + + + + - + -

weighted coil profiles

sum of weighted profiles

Idealised k-space of summed profiles

0th harmonic 1st harmonic

PE

SMASH

data summed with0th harmonic weights

data summed with 1st harmonic weights

easy matrix inversion

=

R

S C

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, …)

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.

Merits of collecting sensitivity data

PPI reconstruction is weighted by coil normalisation

)()/( NrNcrcs jjj

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

www.mr.ethz.ch/sense/sense_method.html

array coil image

body coilraw (array/body)

thresholded raw

filtered thresholdregion grow

local polynomial fit

2/)( ,1,11 bbaa rcrcp

SENSE in difficult regions

coil 1

coil 2

ra

rb

p2

p1

2/)( ,2,22 bbaa rcrcp

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?)