Introduction to kspace based Parallel Reconstruction

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• Introduction to k-space based Parallel
  Reconstruction

Suchandrima Banerjee Parallel Imaging
Seminar,2005 UCSF/UC Berkeley Bioengineering
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Possibilities with Parallel Imaging

• Reduced acquisition times.
• Higher resolution at same acquisition time.
• 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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SMASH(Sodickson et al ,MRM 1997)
Exponential Basis similar to phase encoding
gradients can be synthesized by weighted sum of
coil profiles
-
-






PE
weighted coil profiles
sum of weighted profiles
Idealised k-space of summed profiles
0th harmonic
1st harmonic
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Simulation-SMASH Reconstruction
Conventional Sum-of-Squares
Tailored SMASH (R2)
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PILS Partially Parallel Imaging with Localized
Sensitivities

• Surface coils restrict the bandwidth of signal to
  Yc centered around y0
• FOV in phase encode direction can be reduced to
  Yc without aliasing artifacts

Griswold et al, MRM 2000
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PILS imaging theory

• Reduced FOV images are acquired for multiple
  coils
• Reduction factor is limited by the FOV of each
  coil
• Each surface coil has the same FOV Yc with a
  different offset y0 which spans Y
• Constraint Yc lt Yi lt Y ? so that no overlapping
  of spatial information occurs in the repeating
  subimages of the full FOV reconstruction.
• For each coil element, PILS only reconstructs the
  sub image that lies in the correct position for
  that coil

Griswold et al, MRM 2000
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PILS method/reconstruction

• Determine the correct location of the center and
  width of the coils sensitivity region by
  acquiring 1D coil profile and fitting a sum of
  gaussian functions

• Shift in position (y0) corresponds to
  multiplication of a linear phase term in k-space
• Correctly shifted k-space data is reconstructed,
  resulting in an unaliased full FOV image for each
  coil
• Component coil images are then combined using sum
  of squares

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Coil Sensitivities

• All methods require information about coil
  spatial sensitivities.
• pre-scan (SMASH, g SMASH, SENSE, )
• extracted from data
• (m SENSE, (VD-)AUTOSMASH,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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Auto Calibrating Methods

• Synthesis of missing phase-encoding lines by
  linear combination of data from multiple coils/
  phase encoding lines.
• Combination weights are computed by fitting data
  to additional training lines acquired at the
  center of k-space.
• The training lines also called Auto-Calibrating
  Scan (ACS) lines may be retained in the final
  data matrix to reduce high energy aliasing
  artifacts.

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AUTO and VD-AUTO SMASH
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Computation of combining weights by data fitting
to ACS lines
Jacob et al,MAGMA 1998,Heidemann et al,MRM 2001
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AUTO and VD-AUTO SMASH
Heidemann et al,MRM 2001
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GRAPPA
Griswold et al,MRM 2002
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Data fitting to ACS lines in k-space
AUTO/VD-AUTO-SMASH
GRAPPA
where Nb is the number of blocks used, and A is
the acceleration factor
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Examples of parallel reconstruction

• Offline full recon GRAPPA

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Image
Reconstruction steps at a glance
Signal data
Read Data/order slices
Sign alteration
K-space based parallel recon
Rect FOV?
Multi coil?
Yes
Zero fill
No
Weighted sum of squares
No
Part Fourier?
Yes
Image warping
Homodyne for PF axis, IFFTfilter for FF axis
Scaling
FilterIFFT
Final Image