Parallel Imaging Reconstruction

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Parallel Imaging Reconstruction
Multiple coils - parallel imaging

• Reduced acquisition times.
• Higher resolution.
• Shorter echo train lengths (EPI).
• Artefact reduction.

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K-space from multiple coils
coil views
coil sensitivities
multiple receiver coils
k-space
simultaneous or parallel acquisition
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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
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SENSE reconstruction
ra
p1
coil 1
rb
coil 2
p2
Solve for ra and rb. Repeat for every pixel pair.
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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
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Generalized SMASH
image domain product
k-space convolution
matrix multiplication

R
S
C
gSMASH1 matrix solution
1 Bydder et al. MRM 20024716-170.
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Composition of matrix S
Acquired k-space
coil 1
coil 2
hybrid-space data column
S
FTFE
process column by column
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Coil convolution matrix C
C
FTPE
coil sensitivities
hybrid space
cyclic permutations of
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gSMASH
coil 1

coil 2
S
R
C
requires matrix inversion
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Linear operations

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

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SMASH
-

-





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

R
data summed with 1st harmonic weights
easy matrix inversion
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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.

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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.

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Coil Sensitivities

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

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Pre-scan In data
Merits of collecting sensitivity 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.

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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.

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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
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SENSE in difficult regions
coil 1
coil 2
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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.

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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 gtgt
  speed-up factor.
• Coils should be spatially different.
• (Dont worry about regularisation?)