Parallel MRI: Concepts and Methods - Advance Image Processing in Magnetic Resonance Imaging - page 63

Dynamic low-frequency
images using center 8 lines of
k-space in 4 coils

Resulting dynamically
acquired, self-referenced
sensitivity profiles

Sum of all
low-frequency images

FIGURE 3.2 Sensitivity profile estimation using the center-lines of k -space.

Coil-sensitivity profiles are smoothly varying functions, and can therefore be
assumed to contain only low spatial frequencies. A set of contiguous, low-
frequency k-space lines is acquired with every acquisition in a dynamic
sequence and is used to reconstruct a low-frequency image from each coil (W 1 I LF ,
W 2 I LF , W 3 I LF , W 4 I LF ). The images are then added together to form: (W 1

+ W 2 + W 3 +

W 4 ) I LF . The resulting sensitivity profiles are computed by taking the ratio

of the single-coil low-frequency images, to the sum of the low-frequency coil
images. This approach is shown in Figure 3.2. The low-frequency images
shown on the left are reconstructed using the eight center lines of k-space.

⋅ I LF ≈

3.3.3.2 Parallel MR Image Reconstruction Techniques

In this section, we describe how each of the parallel imaging techniques solves
the linear system shown in Equation 3.2, assuming that the sensitivity profile
information is known.
Two main approaches to solving the linear system of equations shown in
Equation 3.2 have been adopted. The k-space approaches, such as SMASH and
GRAPPA, seek to use partial data acquired in parallel in all the coils, in order to
synthesize a representation of the full k-space of the image. Once this is done,
image reconstruction is performed by usual Fourier reconstruction. Image domain
approaches such as regular SENSE and SPACE RIP solve the linear system of
equations in the image domain.

3.3.3.3 K-Space Approaches

3.3.3.3.1 SMASH
SMASH (7) is dubbed a k-space technique, in the sense that it seeks to estimate a
composite k-space of the image from partial data acquired in different coils. Image
reconstruction is performed by Fourier transformation of the composite k-space.
SMASH operates by using linear combinations of simultaneously acquired signals
from multiple surface coils with different spatial sensitivities.