title: The inversion of 2D NMR relaxometry data using L1 regularization.
abstract: NMR relaxometry has been used as a powerful tool to study molecular dynamics. Many algorithms have been developed for the inversion of 2D NMR relaxometry data. Unlike traditional algorithms implementing L2 regularization, high order Tikhonov regularization or iterative regularization, L1 penalty term is involved to constrain the sparsity of resultant spectra in this paper. Then fast iterative shrinkage-thresholding algorithm (FISTA) is proposed to solve the L1 regularization problem. The effectiveness, noise vulnerability and practical utility of the proposed algorithm are analyzed by simulations and experiments. The results demonstrate that the proposed algorithm has a more excellent capability to reveal narrow peaks than traditional inversion algorithms. The L1 regularization implemented by our algorithm can be a useful complementary to the existing algorithms.
authors.affiliation: Institute of Medical Imaging Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China.
authors.forename: Xiaolong
authors.initials: X
authors.lastname: Zhou
authors.affiliation: Institute of Medical Imaging Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China.
authors.forename: Guanqun
authors.initials: G
authors.lastname: Su
authors.affiliation: Institute of Medical Imaging Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China.
authors.forename: Lijia
authors.initials: L
authors.lastname: Wang
authors.affiliation: Institute of Medical Imaging Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China. Electronic address: nsd4647@163.com.
authors.forename: Shengdong
authors.initials: S
authors.lastname: Nie
authors.affiliation: School of Geosciences in China University of Petroleum, Qingdao 266580, Shandong Province, China.
authors.forename: Xinmin
authors.initials: X
authors.lastname: Ge
keywords: 2D inversion; 2D spectra; FISTA; Low-field NMR