get_acs_lines.m

%% Assignment 2-2: Obtaining the ACS domain.
%% Loading data
%%
brainCoilsData = load('brain_coil.mat');
brainCoils = brainCoilsData.brain_coil_tmp;
%%
[phaseLength, freqLength, channels] = size(brainCoils);
disp(size(brainCoils));  % Phases, Frequencies, Coils
%% Convert to Fourier Domain with 2D Fast Fourier Transform
% Don't forget to use fftshift and ifftshift.

fullKspace = ifftshift(fft2(fftshift(brainCoils)));
%% 
% Checking if k-space was generated correctly.

imagesc(rsos(fullKspace), [0, 10000]);
colormap('gray');
colorbar();
%% Setting parameters for later use.
%%
downSamplingRate = 3;
acsLength = 6;
%% Making the mask
% Creating a mask for the downsampling and the acs lines.

mask = zeros(size(fullKspace));  % Making a mask for the brain coils.

acsStart = floor((phaseLength - acsLength) ./ 2);
acsFinish = acsStart + acsLength;

for i=1:phaseLength  % Goes along the phase encoding axis.
    if rem(i, downSamplingRate) == 0
        mask(i, :, :) = 1;  % Broadcasting the value of 1 to mask(i, :, :).
    end
    
    % Separated the 2 if conditions to make the code more legible.
    if (acsStart < i) && (i <= acsFinish)
        mask(i, :, :) = 1;
    end    
end
assert(isequal(size(mask), size(brainCoils)), 'Mask size is incorrect.')
%% Displaying mask.
% This code functions to check whether the mask has been made correctly.
% 
% White lines indicate 1's. Black lines indicate 0's.
% 
% All values should be either 0 or 1. Thepresence of any other value indicates 
% an error.
% 
% There should be a white band in the middle, with striped lines surrounding 
% it.

dispMask = mean(mask, 3);
imagesc(dispMask);
colormap('gray');
colorbar();
%% Generating the down-sampled k-space image
% Obtain the Hadamard product (elementwise matrix multiplication) between the 
% full k-space data and the mask.
% 
% Hint: use the .* operator, not the * operator, which does matrix multiplication.

% Elementwise (Hadamard) product (multiplication) of matrices.
downSampledKspace = fullKspace .* mask;
assert(isequal(size(downSampledKspace), size(brainCoils)), 'Reconstruction is of the wrong shape.')
%% 
% Visualizing downsampled k-space.

imagesc(rsos(downSampledKspace), [0, 10000]);
colormap('gray');
colorbar();
%% Generating downsampled coil data from downsampled k-space.
%%
dsBrainCoils = ifftshift(ifft2(fftshift(downSampledKspace)));
%%
% Using rsos (root sum of squares) to make visualization possible.
recon = rsos(dsBrainCoils);
original = rsos(brainCoils);
assert(isequal(size(recon), size(original)), 'The reconstruction has an incorrect size.')
%% Final visualization of data.

figure;
colormap('gray');

subplot(1, 2, 1);
imagesc(original);
title('Original Brain Image');
colorbar();

subplot(1, 2, 2);
imagesc(recon);
title('Downsampled Brain Image');
colorbar();
%% Checking for scaling issues.
%%
% Display minima and maxima of original data.
disp(min(recon, [], 'all'));
disp(max(recon, [], 'all'));
disp(min(brainCoils, [], 'all'));
disp(max(brainCoils, [], 'all'));

% Plotting Differences between rsos treated original data and recon data.
figure;
colormap('default');

hold on
histogram(original(:), 100, 'FaceColor','auto');
histogram(recon(:), 100, 'FaceColor','auto');
title('Comparison of Original versus Reconstruction values.')
hold off