NMR Spectra Denoising With Vandermonde Constraints

Nuclear magnetic resonance (NMR) spectroscopy serves as an important tool to analyze chemicals and proteins in bioengineering. However, NMR signals are usually contaminated by noise, affecting subsequent quantitative analysis. Denoising NMR signals has become a long-time concern. The low-rank Hankel matrix assumption has been widely used in NMR denoising due to the damped exponential model of NMR signals in the time domain. In this work, we propose an improved low-rank Hankel matrix reconstruction, CHORD-V, by maintaining the exponential signal form with a Vandermonde factorization. Experimental results show that, under high noise standard deviation 0.06 for ten synthetic data (or ten real human metabolite spectra), CHORD-V reduces the normalized root-mean-square error (NRMSE) by 24% (or 71%), 28% (or 56%), and 8% (or 21%) than typical methods, Cadzow and randomized QR decomposition (rQRd), and the state-of-the-art method, convex Hankel low-rank matrix approximation for denoising exponential signals (CHORD), respectively. For the relative errors of peaks in ten synthetic data, including peak height, position, and correlation, CHORD-V offers the lowest errors 0.039, 0.004, and 0.048 in the signal region, and the smallest error 0.123 for fake peaks in the nonsignal region. All experiments demonstrate that CHORD-V provides the lowest denoising error and the most balanced and better peak criteria.