Transcript Partial Parallel imaging (PPI) in MR for faster imaging

Partial Parallel imaging
(PPI) in MR for faster
imaging
IMA
Compressed Sensing
June, 2007
Acknowledgement: NIH Grants 5RO1CA092004 and 5P41RR008079,
Pierre-Francois Van de Moortele, Gregor Adriany, Kamil Ugurbil
Our coils

Open face coil

16 Channel
“closed” coil
Intrinsically, surface coils offer a representation of signal as
The sensitivities are complex valued
Acquired k-space,
How to INTERPOLATE most stably to the
Non-acquired data.
we will see why it makes completely sense to
think about interpolation
Field of View
Courtesy: Douglas Noll, University of Michigan
Undersampled images
Undersampled individual images
I
unaliased
1
H
1 " reducedFOV "


 S  S  S  y
H
1
The linear system
The solution of the linear system gives rice to a spatially varying noise
amplification. This is solely dependent on the sensitivities and is referred to
as the geometry factor
The geometry factor
α is the index of an aliased pixel,
βn is the index of an unaliased
pixel.
Overall loss when using PPI is SNRred=SNRfull/(g sqrt(R))
The reduced FOV is the RSOS of all the channels with a reduced FOV, only for illu.
Back to the equation
Image space
S indv. Channels. E encoding.
p un-aliased image
K-space
S indv. Channels. E encoding.
p un-aliased image (all in kspace)
Convolution operator
E is known, but we can make the formal separation of S, as follows:
E”acq” includes all of
k-space for the
sensitivities
Two matrix equations, two unknowns

SENSE/SMASH formalism (get one image)
GRAPPA idea, get multiple images. The
interpolation is essentially similar to Kriging
Courtesy: Yeh, et al, MRM Volume 53, Issue 6 , Pages 1383 - 1392
GRAPPA
Reconstructing
the data for
EACH coil
Courtesy: Griswold et al. MRM, 47(6):1202-1210 (2002)
Several reconstruction is found for EACH k-space pointdue to the blocks. A weigthed average is used to compute
just one

ACS (Auto-Calibration Signal) lines (no x)
,l

GRAPPA formula to reconstruct signal
in one channel
where A represents the acceleration factor. Nb is the number of blocks used
in the reconstruction, where a block is defined as a single acquired line and
A-1 missing lines. 4-8 blocks are needed
Temporal sampling
Interleaved/segmented (2)
PE
Interleaved (2)
½ kspace
½ kspace
time
Works well for imaging of static objects.
For dynamic imaging, each image is
not only undersampled, but also
captures a different part of the
“motion”/”change”. The acquisition is
assumed faster than the motion
PSF considerations (generally)


Let us start with imaging
psf  F ()
Standard PPI used to
“unalias” the effects of
the psf
PE or t
UNFOLD (does not require
multichannels)

Specifically, alternate the sampling
by a factor 2, such that
…
½ kspace
Remove aliasing by
Courtesy: Madore. MRM 48:493 (2002).
fMRI (UNFOLD)
Remove aliased
frequency by
selective filtering
FIG. 16. Results obtained for a single-trial fMRI experiment (4 spiral interleaves, 16 kz phase-encode values, axial images, matrix size
128 3 128, TR 5 250 msec, TE 5 40 msec, 5 mm resolution along z, 24 cm FOV). Bilateral finger tapping was performed while a 2 sec audio
cue was on, and then stopped for 12 sec. The acquisition time for a time frame (16 sec) is longer than a paradigm cycle (14 sec). UNFOLD is
used to reduce the acquisition time by a factor 8, providing 7 frames per paradigm cycle. a: The acquired frames are corrupted by an 8-fold
aliasing in the through slice direction. b: Temporal frequency spectrum for the highlighted image point in a. UNFOLD interleaves 8 spectra
into
the same temporal bandwidth. Marks are placed on the axis at the locations of the DC, fundamental and harmonic frequencies for the
non-aliased material. Selecting only these frequencies, the aliasing seen in a is removed in c.
Courtesy: Madore. MRM 48:493 (2002).
Extend the
concept
of
aliasing
Line in image
Unalias the
support in x-f
space, just like we
unalias in x space
with SENSE
Tsao et al, MRM 50: 1031-1042 (2003)
DATA challenge
1.
Where is the support in x-f space?
Interleaved training
set
Used to
define
support in x-f
space
“Equivalent”
to a
reference
scan
Tsao et al, MRM 50: 1031-1042 (2003)
Similar concepts hold
for radial, where the
center is the “prior”.
This is used in speech
imaging
How do the methods compare?
k-t SENSE, vs. Sliding Window

Consensus (in cardiac imaging) of:
Xu et al. MRM, 57:918930 (2007)
What does the artifact mean
Xu et al. MRM, 57:918930 (2007)
Looking at the temporal variation
(in speech
[radial])
Sliding window
K-t SENSE
y
t
Comments/Conclusions
Michael S. Hansen. Workshop on Non-catesian MRI.
2007
Formally
The mising information can be determined from the acquired data,
if the coeeficients a(i,j,k) are known
With localized sensitivities (smooth in image space)
SMASH

Find weights nk(m)(x) [no x –readout dependence] such that we
get a new synthetic sensitivity profile Cmcomp
WE do parallel Imaging by finding ONE combined image (just like SENSE)
m is selected depending on how FAR the data must be interpolated. Only one
line is used to advance the data
Generalised SMASH

Find weights ak(m)(x) [with x –
readout dependence] such that
(x)
Express
s j ( x, k y )   C j  e
q

m  p

ik y y

q
a
m  p
m
j
C j ( x, y) 
( x)   e
q

m  p
a mj ( x)eimky
 i ( k y  mk ) y

a mj ( x)s ( x, k y  mk )
We use several phase-encoding lines to generate missing
information. For each readout point a new set of weights
are comp.
Two severe issues
The final image is that of a complex
sum image of the individual images.
Not optimal for SNR
 Total cancellation can occur with such
complex sums.
 Coils where phase-aligned PRIOR to
reconstruction

AUTO-SMASH

ACS (Auto-Calibration Signal) lines
(no x), not fitting to a harmonic, but
a “missing” PE-line