A new application of compressive sensing in MRI

Image formation in Magnetic Resonance Imaging (MRI) is the procedure which allows the generation of the image starting from data acquired in the so called k-space. At the present, many image formation techniques have been presented, working with different k-space filling strategies. Recently, Compressive Sampling (CS) has been successfully used for image formation from non fully sampled k-space acquisitions, due to its interesting property of reconstructing signal from highly undetermined linear systems. The main advantage consists in greatly reducing the acquisition time. Within this manuscript, a novel application of CS to MRI field is presented, named Intra Voxel Analysis (IVA). The idea is to achieve the so-called super resolution, i.e. The possibility of distinguish anatomical structures smaller than the spatial resolution of the image. For this aim, multiple Spin Echo images acquired with different Echo Times are required. The output of the algorithm is the estimation of the number of contributions present in the same pixel, i.e. The number of tissues inside the same voxel, and their spin-spin relaxation times. This allows us not only to identify the number of involved tissues, but also to discriminate them. At the present, simulated case studies have been considered, obtaining interesting and promising results. In particular, a study on the required number of images, on the estimation noise and on the regularization parameter of different CS algorithms has been conducted. As future work, the method will be applied to real clinical datasets, in order to validate the estimations.