Xiaobo Qu1, Xue Cao2, Di Guo3, Zhong Chen4
1Department of Communication Engineering,, Xiamen University, Xiamen, Fujian, China; 2School Of Software, Shanghai Jiao Tong University, Shanghai, China; 3Department of Communication Engineering, Xiamen University, Xiamen, Fujian, China; 4Department of Physics, Xiamen University, Xiamen, Fujian, China
Multidimensional magnetic resonance spectroscopy (MRS) can provide additional information at the expense of longer acquisition time than 1D MRS. Assuming 2D MRS is sparse in wavelet domain, Iddo first introduced compressed sensing (CS)  to reconstruct multidimensional MRS from partial and random free induction decay (FID) data. However, the darkness in 1D NMR spectra derives from the discrete nature of chemical groups . Significant peaks in these MRS takes up partial location of the full MRS while the rest locations own very small or even no peaks. This type of MRS can be considered to be sparse itself, named sparse MRS. In the concept of sparsity and coherence for CS, we will demonstrate that wavelet is not necessary to sparsify sparse MRS and even makes the reconstructed MRS worse than without wavelet. Furthermore, a lp quasi-norm compressed sensing reconstruction is employed to improve the quality of reconstruction.