MRI: Partial Fourier imaging

Here are routines to reconstruct MR images using an iterative solver. The purpose is to reconstruct images based on data encoded by either spatially linear or nonlinear gradient fields, including PatLoc or O-space imaging.

Definitions

Note: Please refer to the page for the range for k-space coordinates and the strength of spatial encoding magnetic fields (gradients).

MRI reconstruction: partial Fourier imaging

This example reconstructs an image using an eight-channel coil array. It partially samples the k-space data (75% in k_y) with 2x2 accelerations (skipping one k-space sampling in both k_x and k_y) in a rectilinear Cartesian k-space.

K-space sampling pattern

The following codes created two sampling patterns: one had full Fourier sampling (K_general) and the other one had 75% partial Fourier sampling (K_general_pf). Both had the 2x2 acceleration in this example, as specified by R{r_idx}.

           %sampling of gradient-field encoded data
            for g_idx=1:1
                K{g_idx}=zeros(n_phase1,n_freq);
                K{g_idx}(1:R{r_idx}(1):end,1:R{r_idx}(2):end)=1;
                
                [k_phase,k_freq]=ind2sub(matrix{1},find(K{g_idx}));
                
                k_phase=((k_phase-1)-n_phase1./2)./n_phase1.*2;
                k_freq=((k_freq-1)-n_freq./2)./n_freq.*2;
                K_general=[k_phase(:) k_freq(:)];
                
                
                %partial Fourir;
                pf=0.75;
                
                K_general_pf=[k_phase(1:round(length(k_phase(:)).*pf)) k_freq(1:round(length(k_freq(:)).*pf))];
            end;

The partial Fourier sampling had the following pattern.

The reconstructed images are shown below. The left, middle, right ones are without partial Fouerier sampling, with partial Fourier sampling, and the difference (10x amplification for the visualization purpose) between two. Reconstructed images are very similar. However, at the boundary of the FOV had much higher noise in the reconstruction with partial Fourier sampling.