Parallel MRI: Concepts and Methods - Advance Image Processing in Magnetic Resonance Imaging - page 72

3.3.3.4.4.2.2 Choice of the Phase Modulations
To appropriately cover the k -space distribution of the image I(x, y), the choice
of the phase modulations used in the inversion matrix should be influenced by
the frequency content of the sensitivity profile. In the spatial domain, the image
received in a coil having a sensitivity profile W c (x, y) can be written as I c (x, y)

=
I(x, y) W c (x, y). Therefore, the k-space profile of I c (x, y) is the convolution of the
k-space profile I(k x , k y ) of the image I(x, y), with the k -space profile W c (k x , k y ) of
the sensitivity profile W c (x, y). This convolution amounts to a blurring of the k-space
data I(k x , k y ) in an image. Because a different convolution is performed for each
coil, a different blurring of I(k x , k y ) occurs for each coil. Subsampling the convolved
k-space data received in different coils, therefore, results in different coverage of the
k-space of the image I(x, y). Hence, in order to get the best k-space coverage of
I(x, y), it is necessary to optimally sample the k-space data from all the coils. In
contrast to SMASH and SENSE, which require the use of equally spaced k-space
lines, SPACE RIP is completely flexible in this regard. In the following section, we
show how a carefully chosen irregular sampling pattern (whereby the center of k-space
is sampled more densely than the periphery) coupled with appropriate matrix condi-
tioning, would better capture the spatial energy distribution, yielding reconstructions
with higher SNR and fewer artifacts than in other parallel imaging techniques.

3.4 EXAMPLES

The following examples demonstrate each of the preceding algorithms and illus-
trate their effectiveness in removing aliasing artifacts from subsampled parallel
MR acquisitions. The ACR quality phantom data shown here were acquired using
an eight-channel head coil on a GE Signa Lx 1.5-T MR scanner. This phantom
slice provides both a large uniform area to easily identify residual aliasing artifacts
and a set of boxes with varying resolution through which one can measure blur.
For these examples, the full 256 by 256 k-space set was obtained once, then each
of the various subsampling patterns were simulated by excluding those k-space
lines from the reconstruction. To more accurately reflect the current common
practice in parallel MR imaging, the sensitivity maps were estimated using self-
referenced data. In this case, between 8 and 20 lines closest to the lowest fre-
quency in k-space were used to estimate the coil-sensitivity maps. A Gaussian
envelope was applied to this data to filter the high-spatial-frequency components
along the readout direction and to limit ringing along the phase-encode direction,

and the estimates were then normalized. An example of these coil-sensitivity

estimates are shown in Figure 3.10 .

3.4.1 E XAMPLE 1: U NIFORM S UBSAMPLING

Figure 3.11(a) shows a 2x-acceleration uniform subsampling pattern. Figure 3.11(b)

shows the resulting uncorrected image reconstruction using the subsampled data.
The twofold aliasing pattern that parallel MR reconstruction algorithms aim to
suppress is clearly evident.