Fast three-dimensional NMR spectroscopy reconstruction based on Hankel matrix with two-directional sliding windows

Nuclear magnetic resonance (NMR) spectroscopy has grown into a formidable tool in biomedical analysis and quantification. However, the lengthy acquisition for high-dimensional NMR spectroscopy hinders its broader applications. Non-uniform sampling (NUS) effectively reduces the acquisition time by acquiring partial data. Therefore, the need for reconstruction methods is motivated. The low-rank block Hankel matrix reconstruction method achieves notable reconstruction, but requiring prolonged computational time. In this work, a novel two-directional sliding window method is proposed to reduce the size of the low-rank matrix, effectively mitigating the computational time. Incorporating the parallel computation, further acceleration can be achieved. The numerical experiments on synthetic and real NMR spectroscopy illustrate that, among compared approaches, the proposed method accomplishes reconstruction in the shortest time without compromising the spectral quality.