Meeting Banner
Abstract #2813

L1, Lp, L2, and Elastic Net Penalties for Regularization of Two-Gaussian Component Distributions in One-dimensional Magnetic Resonance Relaxometry

Christiana Sabett1, Ariel Hafftka1, Kyle Sexton2, and Richard Spencer2

1Applied Mathematics & Statistics, and Scientific Computation (AMSC), University of Maryland, College Park, College Park, MD, United States, 2National Institute on Aging (NIA), Baltimore, MD, United States

Magnetic resonance (MR) relaxometry time distributions are recovered via the inverse Laplace transform (ILT), an ill-posed problem that is generally stabilized using Tikhonov regularization. Recent work has considered other penalties, such as the L1 penalty for locally narrow distributions. Lp penalties, 1<p<2, may be appropriate for distributions consisting of both narrow and broad components; a linear combination of L1 and L2 penalties, the elastic net (EN), may similarly be useful. However, there is little guidance regarding the choice of regularization penalty for the recovery of transverse relaxation distributions. We compare the effectiveness of each penalty for representative relaxation data.

This abstract and the presentation materials are available to members only; a login is required.

Join Here