Comparing Sparsity Penalty Functions for Combined Compressed Sensing and Parallel MRI

Abstract:

We employ SpRING, a combination of compressed sensing (CS) and parallel imaging, to reconstruct an image from highly undersampled magnetic resonance imaging (MRI) data. Among the growing number of CS algorithms published in the MRI literature, numerous "norms" for promoting sparsity are chosen for various reasons. When developing the SpRING framework, we leave the CS penalty function as a design choice rather than a central feature of the method. We discuss several choices of penalty functions, associating them with different implicit image priors when viewing CS through a Bayesian lens and compare these priors with empirical distributions for both a simulated Shepp-Logan phantom and real anatomical (T_1-weighted MPRAGE) brain data. We perform SpRING reconstructions of undersampled versions of these datasets and use the empirical distribution comparisons to help interpret the results. These simulation results using SpRING demonstrate the importance of choosing an appropriate penalty function for both simulated and real data.

Biography:

Daniel S. Weller received the B.S. degree in electrical and computer engineering from Carnegie Mellon University (CMU), Pittsburgh, PA, in 2006, and the S.M. degree in electrical engineering and computer science (EECS) from the Massachusetts Institute of Technology (MIT), in 2008. He is pursuing the Ph.D. degree in EECS with the Signal Transformation and Information Representation Group, Research Laboratory of Electronics, MIT. He was an undergraduate research assistant with the General Motors Collaborative Research Laboratory at CMU and has completed summer internships at Texas Instruments, Apple, and ATK. He is a member of Tau Beta Pi, Eta Kappa Nu, IEEE, the ISMRM, and SIAM.

He is the recipient of a National Defense Science and Engineering Graduate (NDSEG) fellowship and a graduate research fellowship from the National Science Foundation (NSF). His current research interests include compressed sensing, magnetic resonance imaging, and applications of estimation theory in sampling and signal processing.