A low rank Hankel matrix reconstruction method for ultrafast magnetic resonance spectroscopy

Magnetic resonance spectroscopy has many important applications in bio-engineering while acquiring high dimensional spectroscopy is usually time consuming. Non-uniformly sampling can speed up the data acquisition but the missing data points have to be restored with proper signal models. In this work, a specific two dimensional (2D) magnetic resonance signal, in which the first dimension lies in frequency domain while the second dimension lies in time domain, is reconstructed with a proposed low rank Hankel-matrix method. This method explores two general properties: 1) the rank of a structured matrix, converted from a 2D exponential signal, is equal to the number of 2D spectral peaks; 2) this rank is small if the spectrum is sparse. Results on real magnetic resonance spectroscopy show that proposed method outperforms the state-of-compressed sensing method on recovering low-intensity spectral peaks.