Parsimonious discretization for characterizing multi‐exponential decay in magnetic resonance

• Published in: NMR in biomedicine Vol. 33; no. 12; pp. e4366 - n/a
• Main Authors: Bonny, Jean‐Marie, Traore, Amidou, Bouhrara, Mustapha, Spencer, Richard G., Pages, Guilhem
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 01.12.2020; Wiley
• Subjects: Algorithms; Biological products; Brain - diagnostic imaging; Computer Simulation; cumulative distribution function; Decay; Discretization; Humans; inverse Laplace transform; Inverse problems; Life Sciences; Magnetic resonance; Magnetic Resonance Spectroscopy; Male; Myelin; Myelin Sheath - metabolism; Neuroimaging; Noise; Plateaus; Regularization; Resonance; Signal-To-Noise Ratio; simulation; Water; Young Adult; myelin; simulation; cumulative distribution function; inverse Laplace transform
• ISSN: 0952-3480; 1099-1492; 1099-1492
• DOI: 10.1002/nbm.4366

We address the problem of analyzing noise‐corrupted magnetic resonance transverse decay signals as a superposition of underlying independently decaying monoexponentials of positive amplitude. First, we indicate the manner in which this is an ill‐conditioned inverse problem, rendering the analysis unstable with respect to noise. Second, we define an approach to this analysis, stabilized solely by the nonnegativity constraint without regularization. This is made possible by appropriate discretization, which is coarser than that often used in practice. Thirdly, we indicate further stabilization by inspecting the plateaus of cumulative distributions. We demonstrate our approach through analysis of simulated myelin water fraction measurements, and compare the accuracy with more conventional approaches. Finally, we apply our method to brain imaging data obtained from a human subject, showing that our approach leads to maps of the myelin water fraction which are much more stable with respect to increasing noise than those obtained with conventional approaches. A discretization coarser than that often used in practice and a positivity constraint suffice for stabilizing the estimation of multi‐exponential amplitudes. The amplitudes are better estimated by the plateaus of the cumulative density function derived from the outputs of the nonnegative least squares algorithm. This parsimonious approach leads to improved myelin water fraction estimation.