Abstract #3937

Improved Stability of the Inverse Laplace Transform with Non-negativity Constraints through Extension into a Second Dimension, with Applications to Magnetic Resonance Relaxometry of Tissue

Ariel Hafftka^1,2, 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.

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