A Fast Low Rank Hankel Matrix Factorization Reconstruction Method for Non-Uniformly Sampled Magnetic Resonance Spectroscopy

Multidimensional magnetic resonance spectroscopy (MRS) serves as a valuable tool to analyze metabolites in medical imaging, complex chemical compounds in the chemistry, and protein structures in biology. The data acquisition time, however, is relatively long because it increases exponentially with dimensions. Non-uniform sampling is an effective way to accelerate the data acquisition and a proper reconstruction method is necessary to obtain a full spectra of high quality. A state-of-the-art low-rank Hankel matrix method has shown a great ability to reconstruct the low intensity broad peaks and increase the effective sensitivity of the reconstructed spectra. However, this technology faces the challenge of slow computation time because minimizing the rankness encounters the time-consuming singular value decomposition in the iterative algorithm. This heavily prohibits the method from processing higher dimensional MRS. In this paper, a low-rank matrix factorization method that avoids singular value decomposition is introduced to enable fast MRS reconstruction without sacrificing the spectra quality. Combined with a designed parallel computing architecture, the proposed approach can speed up the computation of low-rank approach with a factor up to 150 and enables reconstructing the challenging 3-D MRS within 15 minutes.