Hypercomplex Low Rank Reconstruction for NMR Spectroscopy

Abstract

Nuclear magnetic resonance (NMR) spectroscopy serves as an important tool to analyze chemicals and proteins in bioengineering. Multi-dimensional NMR offers a major improvement in resolution with multi-dimensional spectrum, but significantly increases data acquisition time and produces hypercomplex data that is difficult to be handled. To reduce this time, non-uniformly sampling can be applied to obtain undersampled data and using a reconstruction approach, such as the state-of-the-art low rank method, to remove the spectral artifacts introduced by undersampling. However, only complex format of signal, including the real and imaginary parts, is considered in previous low rank approach, which is less efficient when dealing with hypercomplex data that has multiple components. To solve this problem, a hypercomplex low rank model is proposed by introducing an adjoint matrix operation and then solved with a fast matrix factorization algorithm. This method explores redundant information among all the components of hypercomplex signal. Using simulated data and real protein data, we demonstrate that the proposed method provides a fast and high-fidelity reconstruction of hypercomplex spectroscopy in fast NMR.