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Project 2: GRAPPA Reconstruction


[TOC]


1. Theory

  • In GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA), extra Nyquist-sampled k-space lines are acquired during the parallel imaging scan and are used to calculate the weighting factors that determine the missing k-space data.

Figure 1. ACS lines

  • As in Figure 2, a GRAPPA weights is firstly estimated using the full-sampled ACS lines. According to the translation invariance property of the weighting matrix, we can compute the missing data using GRAPPA weights.

Figure 2. GRAPPA kernel

graph LR
Full[Fully-sampled k-space]
Full --> Sub["Sub-sampled k-space"]
Sub --> GRAPPA["GRAPPA reconstruction"]
GRAPPA --> Comb["Channel combination"]
Comb --> Final["Final image"]
Loading

Figure 3. Flow chart of GRAPPA reconstruction


2. Results

  • The program execution begins and ends in file project2.m. Function grappa_2d.m realizes the GRAPPA algorithm.

Figure 4. Aliased images, R = 2, ACSLine = 24


Figure 5. Results of GRAPPA reconstruction, R = 2, ACSLine = 24


Figure 6. Aliased images, R = 3, ACSLine = 24


Figure 7. Results of GRAPPA reconstruction, R = 3, ACSLine = 24


Figure 8. Aliased images, R = 4, ACSLine = 24


Figure 9. Results of GRAPPA reconstruction, R = 4, ACSLine = 24


Figure 10. Aliased images, R = 2, ACSLine = 48


Figure 11. Results of GRAPPA reconstruction, R = 2, ACSLine = 48


Figure 12. Aliased images, R = 3, ACSLine = 48


Figure 13. Results of GRAPPA reconstruction, R = 3, ACSLine = 48


Figure 14. Aliased images, R = 4, ACSLine = 48


Figure 15. Results of GRAPPA reconstruction, R = 4, ACSLine = 48