Multi-dimensional magnetic resonance spectroscopy is an important tool for studying molecular structures, interactions and dynamics in bio-engineering. The data acquisition time, however, is relatively long and non-uniform sampling can be applied to reduce this time. To obtain the full spectrum,a reconstruction method with Vandermonde factorization is proposed.This method explores the general signal property in magnetic resonance spectroscopy: Its time domain signal is approximated by a sum of a few exponentials. Results on synthetic and realistic data show that the new approach can achieve faithful spectrum reconstruction and outperforms state-of-the-art low rank Hankel matrix method.
Let @math be a Hankel operator which maps a vector @math to a Hankel matrix @math with @math as follows In particular, we denote the Hankel operator by @math instead of @math in the case @math . The LRHMC @cite_9 is based on the observations that the Hankel matrix @math constructed by the FID @math is low rank if the number of spectral peaks is much smaller than the data points in the whole spectrum. Hence, the reconstruction problem can be formulated as the low rank matrix completion problem where @math is the acquired NUS FID data, @math is an operator of the NUS schedule, @math is the nuclear norm defined as a sum of matrix singular values. The efficiency of LRHMC has been verified on numerical simulations and real MRS data @cite_9 . However, we will present in Section that the Hankel matrix of the FID has Vandermonde factorization and experiment results in Section show that the new approach exploiting Vandermonde factorization can achieve much better reconstruction than LRHMC from the same NUS data.
@cite_9
2109163609
Accelerated multi-dimensional NMR spectroscopy is a prerequisite for high-throughput applications, studying short-lived molecular systems and monitoring chemical reactions in real time. Non-uniform sampling is a common approach to reduce the measurement time. Here, a new method for high-quality spectra reconstruction from non-uniformly sampled data is introduced, which is based on recent developments in the field of signal processing theory and uses the so far unexploited general property of the NMR signal, its low rank. Using experimental and simulated data, we demonstrate that the low-rank reconstruction is a viable alternative to the current state-of-the-art technique compressed sensing. In particular, the low-rank approach is good in preserving of low-intensity broad peaks, and thus increases the effective sensitivity in the reconstructed spectra.