Dynamic MR Image Reconstruction using SToRM

Publication:

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

This code generates the result in result.avi, by solving the optimization problem:

where the notation is described in the SToRM paper. In brief, is the series of MR image frames, is the Fourier under-sampling operator, is the matrix of data samples, is the regularization parameter and is the estimated manifold Laplacian.

Functions called by main.m:

AhAX.m

Code to compute for the conjugate gradient algorithm

Ahb.m

Code to compute for the conjugate gradient algorithm

computeWeights.m

Code to compute the weight matrix from navigator data

XL.m

Code to compute for the conjugate gradient algorithm

Data:

Available at: https://iowa-my.sharepoint.com/personal/jcb_uiowa_edu/_layouts/15/guestaccess.aspx?folderid=0a72e5307778348e9a18a820d9fa3624d&authkey=ARlI1w22gv4KBG9EJ3p-OQo

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.