Simulation-Based Sensitivity Analysis of Regularization Parameters for Robust Reconstruction of Complex Material’s T ₁ − T ₂ ¹H LF-NMR Energy Relaxation Signals

We recently showed, in a simulation study using two artificial signals, that our PDCO (Primal Dual interior method for Convex Objectives) reconstruction algorithm can be efficiently used for the reconstruction of low-field proton nuclear magnetic resonance (¹H LF-NMR) relaxation signals into T₁ (spin–lattice) vs. T₂ (spin–spin) time 2D graphs of a material’s composition. In the present study, for highly complex materials, we demonstrate the PDCO’s reconstruction efficacy for a much wider range of simulated signals with higher complexity and different signal-to-noise ratios (SNR) taken from actual reconstructed ¹H LF-NMR spectroscopy signals of oleic acid and cattle manure. The optimal regularization parameters of the PDCO’s reconstructing algorithm were identified for this large range of simulated LF-NMR signals and noise values. These simulated compact graphical and numerical representations demonstrated ¹H LF-NMR relaxation signals of complex materials can be accurately reconstructed into T₁ − T₂ time graphs of a material’s chemical and morphology. The present study further confirmed that an optimal single set of regulatory parameters for the data reconstruction algorithms could be used for different materials or different batches of the same material.