Improved total variation reconstruction methods for cardiac magnetic resonance imaging

Magnetic resonance imaging (MRI) is a popular imaging modality that allows for noninvasive detection of diseases without the use of ionizing radiation. Every imaging modality comes with its set of challenges and limitations. Since the rate at which data can be collected using an MRI scanner is relatively slow, data undersampling is often employed in order to accelerate acquisitions. This undersampling leads to artifacts in the reconstructed image due to the lack of sufficient data. In this dissertation, novel reconstruction techniques are developed to reconstruct high-quality and artifact-free images using a compressed sensing (CS) formulation. The reconstruction techniques are specifically designed and developed to handle the various challenges that occur in acquiring high-resolution myocardial perfusion images. Since the reconstruction of these images is often time consuming, techniques are developed to allow rapid reconstruction of images. Rapid reconstruction aids in the transition of CS techniques for myocardial perfusion MRI into a tool that is routinely used by clinicians.