Code for the l2-SToRM algorithm published in:

Sunrita Poddar and Mathews Jacob. "Dynamic MRI using smooThness regularization on manifolds (SToRM)." IEEE transactions on medical imaging 35.4 (2016): 1106-1115.

Please cite the above paper if you use the developed code.

Code:

main.m: Please run this code to generate the result in result.avi

The above code solves the optimization problem: min_X ||AX-b||^2 + lambda*trace(XLX') where the notation is described in the SToRM paper.

Functions called by main.m:

1. AhAX.m: Code to compute A'A(X) for the conjugate gradient algorithm
2. Ahb.m: Code to compute A'b for the conjugate gradient algorithm
3. computeWeights.m: Code to compute the weight matrix from navigator data
4. XL.m: Code to compute X*L for the conjugate gradient algorithm

Data:

Available at https://iowa-my.sharepoint.com/personal/jcb_uiowa_edu/_layouts/15/guestaccess.aspx?docid=1916f6f217e024ad8b5b2072adcdb3d79&authkey=Ac73aFG89vEXlOvf0bajhkI

The cardiac data was acquired in the ungated mode on a free-breathing subject using a FLASH sequence. The sampling pattern is a mix of golden angle radial lines and uniform radial navigators (refer to paper). Each frame has 10 radial lines, out of which 6 are golden angle lines and 4 are uniform radial navigator lines. Data for 1000 frames was acquired in around 40 s.

1. S.mat: Sampling pattern saved in a cell of size {1 x number_of_frames}. Example: S{1} contains k-space locations sampled for frame 1. These Cartesian locations are obtained by gridding the original non-cartesian locations.
2. b.mat: Acquired data saved in a cell of size {number_of_frames x number_of_coils}. 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.
3. csm.mat: Estimated coil sensitivity maps of size {image_size x number_of_coils}. Maps are obtained using ESPIRIT algorithm
4. 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 bCom is {(number_of_readouts x number_of_navigator_lines) x number_of_frames}.

Results:

A few frames of the result are saved in the video file result.avi.