demo_gen_subspace.m

%%%%%%
% T2 Shuffling Demo: Generate subspace from EPG-simulated signal evolutions
% of a distribution of T2 values
%
% Jonathan Tamir <jtamir@eecs.berkeley.edu>
% Jan 04, 2016
%
%
addpath src/utils

%% Load flip angles and T2 values
angles = dlmread('data/footsim/flipangles.txt');
myT2vals = load('data/footsim/T2vals', 'T2vals'); % seconds
myT2vals = myT2vals.T2vals;
myT1vals = [1000]*1e-3; % T1 values in seconds

figure(1);
hist(myT2vals * 1000, 100);
xlabel('T2 value (ms)');
ftitle('Distribution of T2 values', 24);
faxis;

%% Simulate and generate basis
T = 80; % echo train length
e2s = 2; % number of intial echoes to skip
TE = 5.688e-3; % echo time
K = 4; % subspace size
N = 256; % maximum number of unique T2 values for training
verbose = false;

%
[U, X, T1vals, T2vals, TE, e2s] = gen_FSEbasis(N, angles, T, e2s, TE, myT1vals, myT2vals, verbose);
Phi = U(:,1:K);

%
figure(2);
plot((e2s+1:T+e2s)*TE*1000, X, 'linewidth', 2);
xlim([TE*1000, TE*1000*T]);
xlabel('Virtual echo time (ms)');
ylabel('Signal value');
ftitle('Signal evolutions for distribution of T2 values', 24)
faxis;

figure(3);
plot(Phi, 'linewidth', 3);
ftitle('Subspace curves', 24)
faxis;

%% Project the signal evolutions onto the subspace
figure(4);
Z = Phi*Phi'*X;
plot((1:T)*TE*1000, Z, 'linewidth', 2);
xlim([TE*1000, TE*1000*T]);
xlabel('Virtual echo time (ms)');
ylabel('Signal value');
ftitle('Projected signal evolutions', 24)
faxis;

err = norm(X(:) - Z(:)) / norm(X(:));
fprintf('Relative norm of error: %.6f\n', err);