Compressed sensing MRI using nonseparable shearlet transform and split Bregman algorithm

We analyze the use of discrete nonseparable shearlet transform for sparse representation of the MRI image. This transform is a non-tight frame, but has excellent localization properties in the spatial domain. Additionally, we exploit the frequency representation of the canonical dual filters of this transform and combine it with the measurement process, carried out in the Fourier domain, to implement the split Bregman algorithm for reconstruction. We compare the performance of the proposed approach to approaches using split Bregman algorithm with curvelets, wavelets and total variation.