parallel imaging reconstruction reduced acquisition times. higher resolution. shorter echo train...
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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
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
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?)