MASTeR: MotionAdaptive SpatioTemporal
Regularization for Accelerated Dynamic MRI 

Introduction: This package provides various MATLAB codes for reconstructing quality
cardiac MR images from highly undersampled kspace 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
complexvalued MR image, is a vector with kspace
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 kspace
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 totalvariation operator for can be
used for spatial sparse representation and linear or motionadaptive 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, motionadaptive
transforms), and more. Consult demo and job files for further details. Reference: ·
M. Salman Asif, Lei
Hamilton, Marijn Brummer,
and Justin Romberg, Motionadaptive spatiotemporal regularization (MASTeR)
for accelerated dynamic MRI, Magnetic Resonance in Medicine, Accepted September 2012. MASTeR models temporal sparsity using
motionadaptive linear transformations between neighboring images. Spatial
transform using dualtree complex wavelet transform (DTCWT) and motion
estimation using phase of DTCWT coefficients. To reproduce the results presented in the paper, run 
job_MASTeR or demo_MASTeR for MASTeR 
job_ktMEMC for kt FOCUSS
with ME/MC 
job_rwt_MASTeR for MASTeR with kt 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: 
kt FOCUSS
with ME/MC: R=4; R=8 
Twochamber results: a)
Ground truth images b)
Region of interest (zoomed in) c)
MASTeR reconstruction
and difference image amplified by 5 at R=6 d)
kt 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)
kt FOCUSS with ME/MC reconstruction and difference image amplified by
5 at R=10 Reconstructed videos: 
kt 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 groundtruth 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 kt 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 

