A Bregman iteration algorithm for shearlet-regularized compressed sensing in MRI

Recently, it has been shown that MRI acquisition can be improved a lot using Compressive Sensing (CS) techniques. In our workwe focus on reconstructing sub-Nyquist sampled MRI data, which we regularize using the shearlet transform. The shearlet transform is credited as providing an optimally sparse frame for representing smooth image regions delineated by edges. Hence, it is a good model for MRI images. The resulting basis pursuit (BP) CS formulation is solved using split Bregman iteration, which splits the BP problem into several easier subproblems. The resulting algorithm allows an exact, parameter-free solution to the constrained BP problem. The results show that the algorithm is able to perform any MRI reconstruction task (sub-Nyquist sampled data or not) and even perform image fusion and resolution enhancement