MASTeR: Motion-Adaptive Spatio-Temporal Regularization
for Accelerated Dynamic MRI
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.
· M. Salman Asif, Lei Hamilton, Marijn Brummer, and Justin Romberg, 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:
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
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 – firstname.lastname@example.org
Last updated: October 13, 2012