Ariel Hafftka1,2, Hasan Celik1, Wojciech Czaja2, and Richard G. Spencer1
1Laboratory of Clinical Investigation, National Institute on Aging, National Institutes of Health, Baltimore, MD, United States, 2Department of Mathematics, University of Maryland, College Park, MD, United States
Magnetic resonance (MR) relaxometry and related
experiments provide useful information about tissues. These experiments reveal the distribution of
a parameter, such as T2-relaxation, in a
sample. The process required to recover the distribution from the
observed data, an inverse Laplace transform (ILT), is highly ill-conditioned,
meaning that small amounts of noise can create huge changes in the solution.
Recent work has shown using simulations that 2D MR experiments result in
a problem substantially more stable than in 1D.
We present a theorem quantifying stability of the ILT and use it to
explain the improved performance in 2D.