MASTeR: Motion-Adaptive Spatio-Temporal Regularization

for Accelerated Dynamic MRI

Introduction:

This package provides various MATLAB codes for reconstructing quality cardiac MR images from highly under-sampled k-space data. The main theme in this work is to exploit spatial and temporal structure/sparsity of the MR images during their reconstruction.

Imaging model: Consider a dynamic MRI setup in which data consist of T images in a cardiac cycle. The vector form of the imaging system for an ^th image can be written as 

 is a complex-valued MR image,  is a vector with k-space measurements of ,  is the encoding matrix which consists of subsampled Fourier transform weighted by coil sensitivity maps, and  is the noise in the measurements.

Recovery problem: To recover image sequence  from all the available k-space data , we solve a convex optimization program of the following general form: 

The first term keeps the signal estimate close to the measurements and the second term promotes certain spatial/temporal sparse structure in . For instance, wavelet transform or total-variation operator for can be used for spatial sparse representation and linear or motion-adaptive temporal differences can be used for temporal sparse representation.

The code provides various options/combinations for sampling schemes, L1/L2 spatial/temporal regularizations (spatial: orthogonal or complex wavelet transform; temporal: frame difference, temporal DFT, motion-adaptive transforms), and more. Consult demo and job files for further details.

Reference:

·       M. Salman Asif, Lei Hamilton, Marijn Brummer, and Justin Romberg, Motion-adaptive spatio-temporal regularization (MASTeR) for accelerated dynamic MRI, Magnetic Resonance in Medicine, Accepted September 2012.

MASTeR models temporal sparsity using motion-adaptive linear transformations between neighboring images. Spatial transform using dual-tree complex wavelet transform (DT-CWT) and motion estimation using phase of DT-CWT coefficients.

To reproduce the results presented in the paper, run

-         job_MASTeR or demo_MASTeR for MASTeR

-         job_ktMEMC for k-t FOCUSS with ME/MC

-         job_rwt_MASTeR for MASTeR with k-t FOCUSS

Code and data:

-      MATLAB code package [.zip]

-      Data and sensitivity maps* (large files >200 MB) [link]

*MRI scan data and sensitivity maps were provided by Lei Hamilton and Marijn Brummer.

Results at different values of reduction/acceleration factor R:

Short axis results:

Reconstructed videos:

-       MASTeR: R=4; R=8

-       k-t FOCUSS with ME/MC: R=4; R=8

Two-chamber results:

a)      Ground truth images

b)      Region of interest (zoomed in)

c)      MASTeR reconstruction and difference image amplified by 5 at R=6

d)      k-t FOCUSS with ME/MC reconstruction and difference image amplified by 5 at R=6

e)      MASTeR reconstruction and difference image amplified by 5 at R=10

f)       k-t FOCUSS with ME/MC reconstruction and difference image amplified by 5 at R=10

 Reconstructed videos:

-       MASTeR: R=6; R=10

-       k-t FOCUSS with ME/MC: R=6; R=10

In each of these videos, first row contains the ground truth, second row contains the reconstructed images, and third row contains differences between the reconstructed and ground-truth images amplified by a factor of 5.

The first column is the intermediate reconstruction before using motion information (i.e., only spatial regularization in MASTeR and without ME/MC in k-t FOCUSS). The second column contains final solution.

Questions or comments: Salman Asif – sasif@gatech.edu

MASTeR © 2012  M. Salman Asif and Justin Romberg

Last updated: October 13, 2012