论文标题
2DNMR数据反转，使用本地改编的多重生正则化
2DNMR data inversion using locally adapted multi-penalty regularization
论文作者
论文摘要
二维核磁共振（NMR）中的关键问题是数据反转的速度和准确性。本文提出了一种具有局部适应正则化参数的多质体方法，以快速准确地反转2DNMR数据。 该方法解决了一个无约束的优化问题，其目标包含数据拟合项，单个$ L1 $惩罚参数和多个参数$ L2 $惩罚。我们提出了快速迭代收缩和阈值（FISTA）方法的改编，以解决多质量最小化问题，以及一个自动程序来计算所有惩罚参数。该过程概括了[Bortolotti等人，\ emph {逆问题}，33（1），2016年]中引入的统一惩罚原则。 所提出的方法使我们能够获得准确的放松时间分布，同时保持短暂的计算时间。关于合成和实际数据的数值实验的结果证明，所提出的方法在重建峰和通常表征NMR弛豫时间分布的峰值和平坦区域有效。
A crucial issue in two-dimensional Nuclear Magnetic Resonance (NMR) is the speed and accuracy of the data inversion. This paper proposes a multi-penalty method with locally adapted regularization parameters for fast and accurate inversion of 2DNMR data. The method solves an unconstrained optimization problem whose objective contains a data-fitting term, a single $L1$ penalty parameter and a multiple parameter $L2$ penalty. We propose an adaptation of the Fast Iterative Shrinkage and Thresholding (FISTA) method to solve the multi-penalty minimization problem, and an automatic procedure to compute all the penalty parameters. This procedure generalizes the Uniform Penalty principle introduced in [Bortolotti et al., \emph{Inverse Problems}, 33(1), 2016]. The proposed approach allows us to obtain accurate relaxation time distributions while keeping short the computation time. Results of numerical experiments on synthetic and real data prove that the proposed method is efficient and effective in reconstructing the peaks and the flat regions that usually characterize NMR relaxation time distributions.
