Feature Augmentation for Numerical Inversion of Multi-exponential Decay Curves

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.