Purpose:

1D GRAPPA imaging reconstruction example

1D GRAPPA reconstruction from an 8-channel head array coil using least-square matrix inversion. The data were simulated from the combination of B1 fields by Biot-Savart's law and anatomical features from MPRAGE sequences.

This example simulated 3-fold acceleration in A/P phase-encoding direction. 4 auto-calibration scan (ACS) lines are used to estimate the GRAPPA reconstruction coefficient using 4-by-3 block, which means 4 (+/-2) phase encoding data and 3 (-1, 0, +1) frequency encoding data were used to fit ACS lines.

code: grappa_8ch_example.m

data: sim_8ch_data.mat

Purpose:

1D SENSE imaging reconstruction example

1D SENSE reconstruction from an 8-channel head array coil using least-square matrix inversion. The data were simulated from the combination of B1 fields by Biot-Savart's law and anatomical features from MPRAGE sequences.

Both SENSE reconstructed image as well as the g-factor maps are calculated.

code: sense_8ch_example.m

data: sim_8ch_data.mat

Purpose:

2D SENSE imaging reconstruction example

2D SENSE reconstruction (2X in L-R and 2X in A-P) from an 8-channel head array coil conjugated gradient iterative solver. The data were from MPRAGE sequences on a 3T scanner.

code: sense2_8ch_cg.m

data: mprage_8ch_slice1.mat

Purpose:

Simple demonstration of SENSE imaging reconstruction.

code: sense_recon_easy.m

data: sense_recon_easy.mat

sense_recon_easy;

Purpose:

Generate the aliasing matrix to relate full-FOV image and accelerated image.

Using specfied sampling vector to generate a 2D aliasing matrix. The sampling vector is a vector of n-entries of either 0 or 1, where 0 indicates no k-space line acquisition and 1 indicates k-space line is acquired in the accelerated scan. For example, a sampling vector of [0 1 0 1 0 1 0 1 0 1] indicate the 2-fold acceleration with 8 phase encoding lines. The aliasing matrix is calculated based on Fourier imaging.

*Note* The center of k-space is at the center of the sampling vector, similar to traditional k-space MRI convention, but different from Matlab defaults.

Matlab code: sense_alias_matrix.m

s=zeros(1,64); %simulate 64 phase-encoding lines
s(1:2:end)=1; %only every other line is acquired in accelerated scan; R = 2.
A=sense_alias_matrix(s,[],'auto_k'); %this is the aliasing matrix

Purpose:

Calculate the g-factor maps of the SENSE acceleration

G-factor is the metric to quantify the amplificaiton of noise power in reconstructing SENSE accelerated image. The detail was presented in Pruessmann's 1999 Magn. Reson. Med. paper. In theory, g-factor is the pixel-by-pixel ratio of the image variance between the SENSE reconstructed image and un-accelerated image. And g-factor depends on: (1) the k-space data trajectory (2) coil sensitivit profiles (3) noise covariance matrix of the array coil.

Matlab code: sense_gfactor.m