Multi-exponential decay curves describe the nuclear magnetic resonance response to radiofrequency exposure. This problem is strongly related to finding a non-negative function given a finite number of noisy values of its Laplace Transform. The solution of this inverse problem takes advantage from a functional modelling of the data. We propose a fitting procedure based on the definition of a meshfree interpolant computed via a variably scaled kernel strategy. A parametric weighted sum of a finite number of exponential terms is introduced to describe the data behaviour; a data-driven procedure estimates its free parameters to scale the kernel, acting as a feature augmentation strategy. The performances of this procedure are investigated on real data sets from nuclear magnetic resonance acquisitions in the context of food science
Feature augmentation for numerical inversion of multi-exponential decay curves / Campagna, Rosanna; Perracchione, Emma. - ELETTRONICO. - 2425:(2022), pp. 1-4. (Intervento presentato al convegno International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2020 tenutosi a Rhodes (GR) nel 17–23 September 2020) [10.1063/5.0081505].
Feature augmentation for numerical inversion of multi-exponential decay curves
Emma Perracchione
2022
Abstract
Multi-exponential decay curves describe the nuclear magnetic resonance response to radiofrequency exposure. This problem is strongly related to finding a non-negative function given a finite number of noisy values of its Laplace Transform. The solution of this inverse problem takes advantage from a functional modelling of the data. We propose a fitting procedure based on the definition of a meshfree interpolant computed via a variably scaled kernel strategy. A parametric weighted sum of a finite number of exponential terms is introduced to describe the data behaviour; a data-driven procedure estimates its free parameters to scale the kernel, acting as a feature augmentation strategy. The performances of this procedure are investigated on real data sets from nuclear magnetic resonance acquisitions in the context of food scienceFile | Dimensione | Formato | |
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LaplaceExtrapolation-1.pdf
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https://hdl.handle.net/11583/2973110