Parallel MRI: Concepts and Methods - Advance Image Processing in Magnetic Resonance Imaging - page 67

Reconstructed

0

Raw Data

b 1

Harmonic Data

even lines

1

b 1

Reconstructed

k−space Data

k y k y

k x k x

0

b L

odd lines

k y

1

b L

k x

coeffs
estimate

k y k y

k x k x

FIGURE 3.5 Data flow diagram for the AUTO-SMASH algorithm.

data acquired necessarily reduces SNR. In considering these issues, the creators
of GRAPPA (11) proposed a combination of VD-AUTO-SMASH and coil-by-
coil SMASH reconstructions (16) in which a full FOV data set for each coil is
produced, and then the final image is constructed by combining the separate coil
data using optimal SNR approaches.
The strategy in GRAPPA is to use multiple k -space lines from multiple coils
to reconstruct a single k -space estimate in each coil. The reconstruction param-
eters are again determined by solving a linear system of equations

L Ν −1

b

∑∑

acs (:, ( mb , )

S k + mk ∆ ) = n S (: kbk

y

− Α∆ ) (3.12)

j y y lj , l y

l =1 b =0

which can be solved by rewriting in matrix form, as in the AUTO-SMASH
case. Here, A represents the acceleration factor, and the coefficients are
indexed over both the number of coils and the number of k-space lines used to

n i mb

(,)

,

construct the linear system. A diagram of the data processing flow is given in

Figure 3.6 .

3.3.3.4.3.4 k-Space Methods Summary
Estimation of missing k -space lines has proved to be a successful strategy in
parallel MR image reconstruction. However, we must emphasize that these
methods are approximations to solving the signal equation. They do not provide
an optimal, in the least-squares sense, solution to the signal equation; rather,
they attempt to simulate the acquisition of the missing k-space lines through
extrapolation.