Magnetic resonance imaging (MRI) is a tool commonly used in clinical and research applications for assessment of brain and related pathology. One common use of MRI is characterization of white matter—the “wiring” of the brain—by diffusion tensor imaging (DTI). In order perform DTI, however, one must scan the same sample multiple times to obtain images each sensitive to diffusion, each in a particular direction; some modern protocols include hundreds of directions being scanned. Particularly, at high resolution in small animal imaging, this approach is very slow and has been known to take 24 hours or more for extremely high resolution models of the brain [1]. As such, an important area of research is methods of reducing the scan time of these protocols. A particularly attractive option is a reconstruction technique known as Compressed Sensing (CS).

CS has a few requirements in order to work which must be looked at before considering it as an option for effective reconstruction of undersampled MRI data. Firstly, the data must be compressible, which can be achieved by having data be sparse in a specific domain [2-4], as we will have M << N samples, where N represents the data we are attempting to reconstruct. The constraint of sparsity provides a way to choose an optimal solution in spite of the missing information. Secondly, the data must be undersampled in an incoherent manner [2-4], so that the result of missing data is a noise-like appearance, and not a coherent image artefact. With these two requirements met, the reconstruction must be performed by an iterative process allowing unacquired data to be estimated based on the assumptions of sparsity and incoherent undersampling artefacts [2, 3]. Given that MRI data can readily adhere to these requirements and there is inherent redundancy present in MRI data, CS is an attractive option and will be explored.