% Code for the publication:

% Sunrita Poddar and Mathews Jacob. "Dynamic MRI using smooThness

% regularization on manifolds (SToRM)." IEEE transactions on medical

% imaging 35.4 (2016): 1106-1115.

% Author: Sunrita Poddar, The University of Iowa

% Date: 24 May 2017

% Code solves the l2-SToRM problem described in the above publication.

% Example here reconstructs a free-breathing ungated cardiac dataset

% using a radial trajectory with navigators.

%%

%==============================================================

% Set the parameters for the dataset

%==============================================================

% Dimension of the data is: n x n x nf x nc

n = 512; % Image dimension is n x n

nf = 1000; % Number of frames

nc = 15; % Number of coils

lambda = 0.5; % Regularization parameter

nn = 2; % Number of neighbours retained in weight matrix

sig = 0.3*10^-4; % Parameter for weight computation

cmn = 4; % Number of navigator lines per frame

%%

%==============================================================

% Load the data

%==============================================================

% S.mat: Sampling pattern saved in a cell of size {1 x nf}

% Example: S{1} contains k-space locations sampled for frame 1

% These Cartesian locations are obtained by gridding the original

% non-cartesian locations

load ('S.mat');

% b.mat: Acquired data saved in a cell of size {nf x nc}

% Example: b{10, 3} contains k-space data acquired by the 3rd coil

% at sampling locations in S{10}

% This Cartesian data is obtained by gridding the original

% non-cartesian data

load ('b.mat');

% csm.mat: Estimated coil sensitivity maps of size {n x n x nc}

% Maps are obtained using ESPIRIT algorithm

load ('csm.mat');

% bCom.mat: Navigator lines (in original non-cartesian co-ordinates)

% The data corresponds to a coil that is close to the heart

% Size of the data is {(n x cmn) x nf}

load ('bCom.mat');

%%

%==============================================================

% Compute the weight matrix

%==============================================================

% Computing the weights using navigator lines

W = computeWeights(bCom,nn,sig);

% Add some small temporal regularization

t = 0.05*(circshift(eye(nf),[0 1]) + circshift(eye(nf),[1 0]));

W = max(W,t);

% Compute the Laplacian matrix as L = D - W

L = sparse(diag(sum(W,1))-W);

clear W bCom

%%

%==============================================================

% Solve the optimization problem: min_X { ||AX-b||^2 + lambda*trace(XLX')}

%==============================================================

% We use the conjugate gradient algorithm to solve:

% A'A(X) + lambda*XL = A'b

% where A is the forward operator consisting of Fourier under-sampling and

% coil-sensitivity maps.

% Compute c = A'b

c = Ahb(b,S,csm,n,nf,nc);

clear b

% Compute the function handle: A'A(X) + lambda*XL

gradX = @(z)(AhAX(z,S,csm,n,nf,nc)+lambda*XL(z,L,n,nf));

% Run the Conjugate Gradient algorithm

X= pcg(gradX,c(:),10^-10,40);

%%

%==============================================================

% Reshape the images for viewing and save

%==============================================================

X = abs(reshape(X,n,n,nf));

X = fftshift(fftshift(X,1),2);

save('result.mat', 'X', '-v7.3');