Fast Three-Dimensional NMR Spectrum Reconstruction Using a Block Hankel Matrix Based on Sliding Windows

Nuclear Magnetic Resonance (NMR) spectroscopy is one of the most promising analytical chemistry techniques, although it takes a long time to acquire data. Three-dimensional NMR spectra offer higher resolution. The Low Rank Hankel Matrix (LRHM) method reconstructs three-dimensional undersampled NMR data by transforming each 2D indirect plain slice into a block Hankel matrix. However, this reconstruction process involves a considerable time overhead. In this work, we introduce a block Hankel matrix based on a sliding window method specifically designed for 3D NMR, to accelerate spectrum reconstruction from NUS signals. This approach can effectively reduce the size of the Hankel matrix for faster reconstruction. Experiments on both synthetic and real data demonstrate that the proposed method achieves the fastest reconstruction speed compared to other methods, without compromising the quality of the spectra.