Two-Dimensional Laplace NMR Reconstruction through Deep Learning Enhancement

Laplace NMR is a powerful tool for studying molecular dynamics and spin interactions, providing diffusion and relaxation information that complements Fourier NMR used for composition determination and structure elucidation. However, Laplace NMR demands sophisticated signal processing algorithms such as inverse Laplace transform (ILT). Due to the inherently ill-posed nature of ILT problems, it is generally challenging to perform satisfactory Laplace NMR processing and reconstruction, particularly for two-dimensional Laplace NMR. Herein, we propose a proof-of-concept approach that blends a physics-informed strategy with data-driven deep learning for two-dimensional Laplace NMR reconstruction. This approach integrates prior knowledge of mathematical and physical laws governing multidimensional decay signals by constructing a forward process model to simulate relationships among different decay factors. Benefiting from a noniterative neural network algorithm that automatically acquires prior information from synthetic data during training, this approach avoids tedious parameter tuning and enhances user friendliness. Experimental results demonstrate the practical effectiveness of this approach. As an advanced and impactful technique, this approach brings a fresh perspective to multidimensional Laplace NMR inversion.