Image Processing Reference
In-Depth Information
with the different sets computed, whereby in each reconstruction, one
column location along the
x
axis is optimal. The N optimal columns are
combined in order to get the final image. This procedure increases the compu-
tational load by a factor of N, and can be reduced by assuming that multiple
locations along the frequency-encoded direction can have the same fitting
parameters.
a(x)
k
m
3.3.3.3.2 AUTO-SMASH
One of the significant difficulties with implementing SMASH clinically is that
the reconstruction quality is greatly dependent on the coil configuration used.
Compounding this difficulty is the fact that coil sensitivities are only approxi-
mately known. Thus, more recent k-space methods have focused on bypassing
the need to estimate coil-sensitivity maps.
The first such approach was AUTO-SMASH (14), in which one additional
line of k-space is acquired in the low-frequency region. The harmonic fit coeffi-
cients are then determined by fitting the acquired lines of k-space to this auto-
calibration line. Specifically, the k-space extrapolation coefficients,
a
(m)
are deter-
mined via solution of a linear system of equations:
L
L
∑∑
Sk
comp
(
+
mk
∆
)
=
bSk
(
)
=
aS
ACS
(
kmk
+∆
)
(3.10)
()
m
()
m
y
y
l
l
y
k
l
y
y
l
=
1
l
=
1
This expression can be written in matrix form as
S
(..
kmk
+
∆
)
1
y
y
Skmk
(..,
+
∆
)
=
()
m
()
m
•
S
comp
(:,
k
+
mk
∆
)
b
b
b
()
m
2
y
y
(3.11)
y
y
1
2
L
Skmk
(..,
+
∆
)
L
y
y
where and represent vectors from the acquired
k-space data set. The reconstructed image is formed using these coefficients in the
same fashion as the original SMASH reconstruction equations. A schematic
S
comp
(:,
k
+
mk
∆
)
Sk mk
l
(:,
+
∆
)
y
y
y
y
describing the data flow in AUTO-SMASH is shown in
Figure 3.5
.
This approach can be extended to variable density strategies as well through
the use of additional autocalibration lines, VD-AUTO-SMASH (15).
3.3.3.3.3 GRAPPA
In MR, there is significant concern in maximizing SNR in the received signal.
This is due to the fact that the ratio of spins contributing to the recorded signal
is on the order of 10
−3
. Accelerating the acquisition by reducing the amount of
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