Accelerating multi-echo T2 weighted MR imaging: analysis prior group-sparse optimization.

This works addresses the problem of reconstructing multi-echo T2 weighted MR images from partially sampled K-space data. Previous studies in reconstructing MR images from partial samples of the K-space used Compressed Sensing (CS) techniques to exploit the spatial correlation of the images (leading to sparsity in transform domain). Such techniques can be employed to reconstruct the individual T2 weighted images. However, in the current context, the different images are not independent; they are images of the same cross section, and hence are highly correlated. In this work, we not only exploit the spatial correlation within the image, but also the correlation between the images to achieve even better reconstruction results. For individual MR images, CS based techniques lead to a sparsity promoting optimization problem in a transform domain. In this paper, we show how to extend the same framework in order to incorporate correlation between images leading to group sparsity promoting optimization. Group sparsity promoting optimization is popularly formulated as a synthesis prior problem. The synthesis prior formulation for group sparsity leads to superior reconstruction results compared to ordinary sparse reconstruction. However, in this paper we show that when group sparsity is framed as an analysis prior problem the reconstruction results are even better for proper choice of the sparsifying transform. An interesting observation of this work is that when the same sampling pattern is used to sample the K-space for all the T2 weighted echoes, group sparsity does not yield any noticeable improvement, but when different sampling patterns are used for different echoes, our proposed group sparsity promoting formulation yields significant improvement (in terms of Normalized Mean Squared Error) over previous CS based techniques.