Rank-One-Approximated Decomposition for N-dimensional NMR Spectroscopy Reconstruction with Physical Intelligent Neural Network

Motivation: Low-rank methods can reconstruct multi-dimensional NMR spectra with high quality but need huge time. Goal(s): Develop a robust and high efficient deep learning method based on the low-rank prior. Approach: We utilize the rank-one property of the exponential function in each dimension of NMR spectra and propose Rank-One Approximated Decomposition (ROAD) network. ROAD consists of four modules for peak retrieval, fast rank-one approximation, data consistency and factor matrix update module. Results: Compared to other methods, experiments on synthetic 2D signals and realistic 3D/4D NMR signals show that ROAD can reconstruct signals with less error and preserve low-intensity peaks more reliably. Impact: Designed by fast low-rank approximation, neural network correction and peak retrieval, ROAD shows the robust reconstruction benefited from optimization and fast computation from deep learning. Instead of reconstructing high-dimensional signals directly, ROAD reconstructs signals in each dimension with high efficiency.