Optimization Methods for Magnetic Resonance Image Reconstruction: Key Models and Optimization Algorithms

The development of compressed-sensing (CS) methods for magnetic resonance (MR) image reconstruction led to an explosion of research on models and optimization algorithms for MR imaging (MRI). Roughly 10 years after such methods first appeared in the MRI literature, the U.S. Food and Drug Administration (FDA) approved certain CS methods for commercial use, making CS a clinical success story for MRI. This article reports on several key models and optimization algorithms for MR image reconstruction. Included are both methods that the FDA has approved for clinical use and more recent methods being considered in the research community that use data-adaptive regularizers. It presents in a single survey the many algorithms devised to exploit the structure of the system model and regularizers used in MRI.