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Parsimonious discretization for characterizing multi‐exponential decay in magnetic resonance

Abstract : 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.
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Submitted on : Monday, August 31, 2020 - 3:37:26 PM
Last modification on : Tuesday, August 24, 2021 - 12:30:02 PM


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J.-M. Bonny, Amidou Traore, Mustapha Bouhrara, Richard Spencer, Guilhem Pagès. Parsimonious discretization for characterizing multi‐exponential decay in magnetic resonance. NMR in Biomedicine, Wiley, 2020, 33 (12), ⟨10.1002/nbm.4366⟩. ⟨hal-02926295⟩



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