Entropy aided K-t Group Sparse SENSE method for highly accelerated dynamic MRI by Muhammad Usman, Claudia Prieto, Tobias Schaeffter, and Philip G. Batchelor. The abstract reads:
Over the last few years, the combination of Compressed sensing (CS) and parallel imaging have been of great interest to accelerate MRI. For dynamic MRI, K-t sparse SENSE (K-t SS) has been proposed  for combining the CS based K-t Sparse method  with SENSE. Recently, K-t group sparse method (K-t GS)  has been shown to outperform K-t Sparse for single coil reconstruction, by exploiting the sparsity and the structure within the sparse representation (x-f space) of dynamic MRI. In this work, we propose to extend K-t GS to parallel imaging acquisition in order to achieve higher acceleration factors by exploiting the spatial sensitive encoding from multiple coils. This approach has been called K-t group Sparse SENSE (K-t GSS). In contrast with the previous single-coil based K-t GS method for which a performance parameter is manually optimized for every frequency encode; we propose an entropy based scheme for automatic selection of this parameter. Results from retrospectively undersampled cardiac gated data show that K-t GSS outperformed K-t sparse SENSE at high acceleration factors (up to 16 fold).
K-T Group Sparse Using Intensity Based Clustering by Muhammad Usman, Claudia Prieto, Tobias Schaeffter, and Philip G. Batchelor. The abstract reads:
Over the last years, Compressed Sensing has been of great interest to accelerate dynamic MRI [1-4]. The recently introduced k-t Group Sparse (k-t GS) method  exploits not just the sparsity of dynamic MRI but also the spatial group structure of its sparse representation (x-f space). The reconstruction is done by solving a mixed L1-L2 norm minimization that enforces sparsity in the group selection. K-t GS achieves higher acceleration factors compared to the conventional k-t Sparse method [1-2]. However, it presents two drawbacks: a) an additional training scan is required to assign the groups in x-f space, and b) the group assignment is based only on the connectivity of neighbouring pixels using a time consuming hard thresholding scheme. In this work we propose to modify k-t GS by using the sorted intensity of the sparse representation, estimated from the same acquired data, for group assignment. With this approach groups are assigned by clustering the expected intensity distribution of the x-f space and not the spatial structure of the x-f space as in k-t GS. We have called this approach k-t Group Sparse using Intensity based clustering (k-t GSI) and it has been tested in cine and perfusion cardiac images.
Credit NASA, the last launch of Endeavor (STS-134)