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Magnetic resonance spectroscopy (MRS) has many important applications in medical imaging, biology, and chemistry. The 1-D MRS is too crowded for complex samples to retrieve chemical or biological information. The 2-D MRS unfolds the spectrum by introducing another dimension at the cost of much longer data acquisition time. To speed up the data acquisition, one typical way is to sparsely acquire measurements and then reconstruct the spectrum from incomplete observations. Recently, a low rank Hankel matrix (LRHM) approach has shown great potential to reconstruct the spectrum basing on the assumption that the number of spectral peaks is much less than the number of acquired data points. However, low-intensity spectral peaks are compromised in the reconstruction when the data are highly undersampled. In this paper, a weighted LRHM approach is proposed to tackle this problem. A weighted nuclear norm is introduced to better approximate the rank constraint, and a prior signal space is estimated from the prereconstruction to reduce the unknowns in reconstruction. Experimental results on both synthetic and real MRS data demonstrate that the proposed approach can reconstruct low-intensity spectral peaks better than the state-of-the-art LRHM method.

Improved Reconstruction of Low Intensity Magnetic Resonance Spectroscopy With Weighted Low Rank Hankel Matrix Completion