Parallel MRI: Concepts and Methods - Advance Image Processing in Magnetic Resonance Imaging - page 68

Reconstructed

Raw Data Coil Data

Reconstructed

Image Space Data

k k

k k Root Sum

of Squares

k

k

coeffs

estimate

k k

k k

FIGURE 3.6 Data flow diagram for the GRAPPA algorithm.

3.3.3.4 Image Domain Approaches

3.3.3.4.1 SENSE
As originally presented, the Cartesian form of SENSE (8) is founded upon a uniform
downsampling pattern. Based on the subsequent aliasing pattern that results from
this subsampling choice, one can construct a small system for each spatial-domain
pixel in the acquired data reference frame. Solving this small system gives unaliased
spatial-domain pixels. This process is then repeated for each pixel in the FOV.
For example, consider a multiple coil acquisition employing a “uniform
downsampling by 2” phase-encode k -space acquisition pattern. In the spatial
domain, this sampling pattern will alias a pixel Ι ( j , x ) with a pixel from the

alternate half of the FOV, N /2, x ), as shown in Figure 3.7.

To reconstruct the image, SENSE seeks to identify these two pixel values,
[ I ( j , x ), I ( j

Ι ( j +

+ N / 2 , x )] T , for each pixel location in the acquired subsampled—and,

Sampled at the Nyquist Rate Sampled at one-half the Nyquist Rate

FIGURE 3.7 Diagram of uniform down sampling by 2 and associated aliasing pattern.