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script_vudu_gre.m
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%--------------------------------------------------------------------------
%% load undersampled EPI data at R=3, AP encoding in shot1, PA in shot2
%% (after ghost correction, and removal of readout oversampling)
%% 2021 07 01
%--------------------------------------------------------------------------
addpath utils/
load data/Img_epi_ap.mat
load data/Img_epi_pa.mat
load data/receive.mat % espirit coil sensitivity estimated from reference flash data
mosaic( rsos(Img_epi_ap(:,:,:,:),3), 4, 6, 1, 'ap @ R=3', [0,1e-3], 90 )
mosaic( rsos(Img_epi_pa(:,:,:,:),3), 4, 6, 2, 'pa @ R=3', [0,1e-3], 90 )
% signal norm ratio:
norm2(Img_epi_pa) / norm2(Img_epi_ap)
%--------------------------------------------------------------------------
%% forward model for subsampled data
%--------------------------------------------------------------------------
[N(1), N(2), num_chan, num_slice] = size(Img_epi_ap);
Ry = 3; % accl factor
del_ky = [0,1]; % delta_ky shift between shots
A = fftc(eye(N(2)),1);
A_ap = A(1+del_ky(1):Ry:end,:);
A_pa = A(1+del_ky(2):Ry:end,:);
% (x,y,chan,ap/pa,slc,dwi)
img_use = cat(4, permute(Img_epi_ap, [1,2,3,6,4,5]), permute(Img_epi_pa, [1,2,3,6,4,5]));
% (x, ky, chan) subsampled data
sgnl_ap = zeross([N ./ [1,Ry], num_chan, num_slice]);
sgnl_pa = zeross([N ./ [1,Ry], num_chan, num_slice]);
tic
for nslc = 1:num_slice
for xn = 1:N(1)
m_ap = sq( img_use(xn,:,:,1,nslc) );
m_pa = sq( img_use(xn,:,:,2,nslc) );
% signal in x,ky,chan
sgnl_ap(xn, :, :, nslc) = A_ap * sq(m_ap);
sgnl_pa(xn, :, :, nslc) = A_pa * sq(m_pa);
end
end
toc
%--------------------------------------------------------------------------
%% Sense for AP and PA separately without B0 model
%--------------------------------------------------------------------------
sens = permute(receive, [1,2,4,3]);
lambda_tik = 1e-6; % tikhonov regularization parameter
img_sense = zeross([N, 2, num_slice]);
tic
% recon middle slice
for nslc = 16%1:num_slice
disp(['slice: ', num2str(nslc), ' / ', num2str(num_slice)])
for xn = 1:N(1)
AC_ap = zeross([num_chan * N(2) / Ry, N(2)]);
AC_pa = zeross([num_chan * N(2) / Ry, N(2)]);
for c = 1:num_chan
AC_ap(1 + (c-1)*N(2)/Ry : c*N(2)/Ry, :) = A_ap * diag( sens(xn,:,nslc,c) );
AC_pa(1 + (c-1)*N(2)/Ry : c*N(2)/Ry, :) = A_pa * diag( sens(xn,:,nslc,c) );
end
[U_ap, S_ap, V_ap] = svd(AC_ap, 'econ');
[U_pa, S_pa, V_pa] = svd(AC_pa, 'econ');
Einv_ap = V_ap * diag(diag(S_ap) ./ (diag(S_ap).^2 + lambda_tik)) * U_ap';
Einv_pa = V_pa * diag(diag(S_pa) ./ (diag(S_pa).^2 + lambda_tik)) * U_pa';
rhs_ap = sgnl_ap(xn, :, :, nslc);
rhs_ap = rhs_ap(:);
img_sense(xn,:,1, nslc) = Einv_ap * rhs_ap;
rhs_pa = sgnl_pa(xn, :, :, nslc);
rhs_pa = rhs_pa(:);
img_sense(xn,:,2, nslc) = Einv_pa * rhs_pa;
end
end
toc
img_sense = apodize(img_sense); % perform k-space apodization
nslc = 16; % slices to display
mosaic(img_sense(:,:,1,nslc),1,1,11, 'sense ap', [0,1.5e-3],90)
mosaic(img_sense(:,:,2,nslc),1,1,12, 'sense pa', [0,1.5e-3],90)
mosaic(fft2call(img_sense(:,:,1,nslc)).^.5,1,1,1, 'ap k-space', [0,5e-2],0), setGcf(.5)
mosaic(fft2call(img_sense(:,:,2,nslc)).^.5,1,1,2, 'pa k-space', [0,5e-2],0), setGcf(.5)
%--------------------------------------------------------------------------
%% Vudu joint recon with Hankel low-rank constraint
%--------------------------------------------------------------------------
load data/img_fieldmap.mat % field map estimated using Topup
scale_fleet = norm2(img_sense(:,:,2,:)) / norm2(img_sense(:,:,1,:)); % scale factor between the two shots
esp = 3.3e-4; % echo spacing in ms
t_axis_ap = [0:Ry:N(2)-1] * esp;
t_axis_pa = t_axis_ap(end:-1:1);
winSize = [1,1] * 11;
step_size = 0.5;
num_shot = 2;
use_scaling = 1;
vc = 0;
lambda_msl = (1+vc);
num_iter = 100;
tol = 0.1;
keep = 1:floor(lambda_msl*prod(winSize));
img_vudu = zeross([N,2,num_slice]);
tic
for nslc = 16%1:num_slice
disp(['slice: ', num2str(nslc)])
% create and store encoding matrices
AWC_ap = zeross([N(2)*num_chan/Ry, N(2), N(1)]);
AWC_pa = zeross([N(2)*num_chan/Ry, N(2), N(1)]);
AWC_apH = zeross([N(2), N(2)*num_chan/Ry, N(1)]);
AWC_paH = zeross([N(2), N(2)*num_chan/Ry, N(1)]);
AWC_apN = zeros(size(AWC_ap, 2), size(AWC_ap, 2), size(AWC_ap, 3));
AWC_paN = zeros(size(AWC_pa, 2), size(AWC_pa, 2), size(AWC_pa, 3));
AWC_apHrhs = zeros(size(AWC_apH, 1), size(AWC_apH, 3));
AWC_paHrhs = zeros(size(AWC_paH, 1), size(AWC_paH, 3));
for xn = 1:N(1)
b0 = img_fieldmap(xn,:,nslc) * 2 * pi;
W_ap = exp(1i * t_axis_ap.' * b0);
AW_ap = A_ap .* W_ap;
W_pa = exp(1i * t_axis_pa.' * b0);
AW_pa = A_pa .* W_pa;
for c = 1:num_chan
AWC_ap(1 + (c-1)*N(2)/Ry : c*N(2)/Ry, :, xn) = AW_ap * diag( sens(xn,:,nslc,c) );
AWC_pa(1 + (c-1)*N(2)/Ry : c*N(2)/Ry, :, xn) = AW_pa * diag( sens(xn,:,nslc,c) );
end
AWC_apH(:,:,xn) = AWC_ap(:,:,xn)';
AWC_paH(:,:,xn) = AWC_pa(:,:,xn)';
AWC_apN(:, :, xn) = AWC_apH(:,:,xn) * AWC_ap(:,:,xn);
AWC_paN(:, :, xn) = AWC_paH(:,:,xn) * AWC_pa(:,:,xn);
rhs_ap = sgnl_ap(xn, :, :, nslc);
AWC_apHrhs(:,xn) = AWC_apH(:,:,xn) * rhs_ap(:);
rhs_pa = sgnl_pa(xn, :, :, nslc);
if use_scaling
rhs_pa = rhs_pa / scale_fleet;
end
AWC_paHrhs(:,xn) = AWC_paH(:,:,xn) * rhs_pa(:);
end
% initialize with sense solution:
img_sense_ap = sq(img_sense(:,:,1,:,:));
img_sense_pa = sq(img_sense(:,:,2,:,:));
im_rec = permute(cat(3, img_sense_ap(:,:,nslc), img_sense_pa(:,:,nslc)), [2,3,1]);
for iter = 1:num_iter
im_prev = im_rec;
for xn = 1:N(1)
im_rec(:,1,xn) = im_rec(:,1,xn) - step_size * ( AWC_apN(:,:,xn) * im_rec(:,1,xn) - AWC_apHrhs(:, xn) );
im_rec(:,2,xn) = im_rec(:,2,xn) - step_size * ( AWC_paN(:,:,xn) * im_rec(:,2,xn) - AWC_paHrhs(:, xn) );
end
im_rec = permute(im_rec, [3,1,2]);
if vc
im_rec = cat(3,im_rec, conj(im_rec));
end
A = Im2row( fft2call(im_rec), winSize );
[U, S, V] = svd(A, 'econ');
A = U(:,keep) * S(keep,keep) * V(:,keep)';
k_pocs = Row2im(A, [N, num_shot*(vc+1)], winSize);
im_rec_disp = ifft2call(k_pocs);
im_rec_disp = im_rec_disp(:,:,1:num_shot);
im_rec = permute(im_rec_disp, [2,3,1]);
update = rmse(im_prev,im_rec);
if ~mod(iter,10)
mosaic(im_rec_disp, 1, 2, 100+vc, ['iter: ', num2str(iter), ' update: ', num2str(rmse(im_prev,im_rec))], genCaxis(im_rec), 90)
end
if update < tol
break
end
end
img_vudu(:,:,:,nslc) = permute(im_rec, [3,1,2]);
end
toc
img_vudu = apodize(img_vudu); % perform k-space apodization
mosaic(mean(abs(img_vudu(:,:,1,nslc,1)),3), 1, 1, 21, 'vudu ap', [0,1.5e-3], 90)
mosaic(mean(abs(img_vudu(:,:,2,nslc,1)),3), 1, 1, 22, 'vudu pa', [0,1.5e-3], 90)