Inverse Laplace Transform of Multidimensional Relaxation Data Without Non-Negativity Constraint
Inverse Laplace Transform of Multidimensional Relaxation Data Without Non-Negativity Constraint
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DOI：
10.1021/ct3001393
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发表时间：
2012-10-01
影响因子：
5.5
通讯作者：
Roberts, Peter J.
中科院分区：
文献类型：
--
作者：
Granwehr, Josef;Roberts, Peter J.
描述了一种基于广义形式的吉洪诺夫正则化的算法，用于执行多维数据的拉普拉斯逆变换，而无需频谱条件的非负（NN）约束。使用均匀惩罚（UP）正则化来减少对神经网络的要求，并针对频谱的过零（ZC）引入进一步的惩罚。该 ZC 项用曲线的斜率进行加权，这不会阻止频谱中的负模式，但会使窄峰附近的非物理下冲更加昂贵。使用合成数据证明了该算法的性能，并讨论了计算正则化矩阵的自由参数的优化。
An algorithm based on Tikhonov regularization in generalized form is described to perform an inverse Laplace transform of multidimensional data without a non-negativity (NN) constraint for spectrum conditioning. Uniform penalty (UP) regularization is used to reduce the requirement for NN, and a further penalty is introduced for zero-crossing (ZC) of the spectrum. This ZC term is weighted with the slope of the curve, which does not prevent negative modes in the spectrum but makes nonphysical undershooting in the vicinity of narrow peaks more expensive. The performance of this algorithm is demonstrated using synthetic data, and the optimization of the free parameters for calculating the regularization matrix is discussed.