Image Processing Reference
In-Depth Information
direction G x . This results in M samples acquired at the Nyquist rate of the specified
resolution along the x direction. Acquiring more samples than M, however, at the
same sampling rate, amounts to adding more dependent equations to the linear
system, resulting in increasing the resolution of the image in the x direction, if that
resolution is set, and comes at a higher computational cost without real benefit. In
practice, the user specifies the size of the FOV as well as the number of pixels in
all directions. The gradient magnitude G x is then automatically computed by the
scanner to provide M samples on the time axis. Each acquired signal can therefore
be considered as providing M independent equations in the linear system that we
seek to solve. In order to get M
P independent equations, the values of G y
and G z need to be varied N and P times respectively. Hence, N
×
N
×
P phase-encoding
steps should be performed in order to solve for the image I(m, n, p).
×
3.3.3
P ARALLEL I MAGING M ETHODS
In parallel imaging, the sensitivity profiles of the receiver coils {W k } are used as
complementary encoding functions to phase encoding, a role that is not played
in Fourier imaging. Each sensitivity profile, W k , provides an additional indepen-
dent view of the image, and hence knowledge of these profiles is necessary in
order to resolve the system of equations.
3.3.3.1
Coil-Sensitivity Estimation
A preliminary requirement for almost all parallel imaging techniques is the knowl-
edge of the coil-sensitivity profiles, W k . A number of approaches have been adopted
in order to estimate these profiles, based on solving Equation 3.2 for W k (x, y).
3.3.3.1.1 Static Estimate
The static estimate assumes that the coil-sensitivity profile is constant during the
imaging procedure and is most accurate when the imaging coils are fixed. A
calibration scan is done prior to the initiation of parallel imaging whereby a full
k -space data set is acquired with all the coils, and the images are reconstructed.
The resulting images are weighted by the coil-sensitivity profiles W k (x, y)
I(x, y).
An extra scan is performed using the body coil of the scanner where it is assumed
that the sensitivity profile is W k (x, y)
=
1. The resulting image is I(x, y). Taking
the ratio of the two images yields W (x, y) for all the coils. Figure 3.1 shows a
k
four-element array example. Full k-space images are shown.
For the case when coils are arranged around the FOV, it is common to assume
that the combined sensitivity profile is homogeneous. This means that adding the
images in all the coils results in I(x, y). If this assumption is valid, there is no
need to acquire an additional image using the body coil.
3.3.3.1.2 Dynamic Self-Calibrated Estimate
The dynamic self-calibrated sensitivity profile estimates consider that the coil
sensitivity varies during the dynamic scans, and seeks to compute it dynami-
cally from a small number of k-space lines acquired during parallel imaging.
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