Sparse Models and Multiple Receivers

Magnetic resonance imaging (MRI) is an increasingly versatile diagnostic tool for a variety of medical purposes. During a conventional MRI scan, samples are acquired along a trajectory in the spatial Fourier transform domain (called k-space) and the image is reconstructed using an inverse discrete Fourier transform. The affordability, availability, and applications of MRI remain limited by the time required to sam-ple enough points of k-space for the desired field of view (FOV), resolution, and signal-to-noise ratio (SNR). GRAPPA, an accelerated parallel imaging method, and compressed sensing (CS) have been successfully employed to accelerate the acquisi-tion process by reducing the number of k-space samples required. GRAPPA leverages the different spatial weightings of each receiver coil to undo the aliasing from the re-duction in FOV induced by undersampling k-space. However, accelerated parallel imaging reconstruction methods like GRAPPA amplify the noise present in the data