L1-based正则化方法分析四极峰FFC色散分布
An automatic L1-based regularization method for the analysis of FFC dispersion profiles with quadrupolar peaks
摘要：
快速场循环核磁共振弛豫法是一种非破坏性的技术，用于研究具有广泛应用的系统的分子动力学和结构，如环境，生物学和食品。除了大量的文献中的建模和应用这种技术在特定领域，相关的参数识别问题的算法方法仍然缺乏。我们相信，一个强大的算法方法将允许在几个应用领域的不同样品的统一处理。在本文中，我们模型的参数识别问题的约束$L_1$正则化非线性最小二乘问题。按照[Analytical Chemistry 2021 93（24）]中提出的方法，非线性最小二乘法项通过将获得的弛豫曲线分解为与1H-1H和1H-14 N偶极-偶极相互作用相关的弛豫贡献来实现数据一致性。数据拟合和基于L1的正则化项通过所谓的正则化参数来平衡。对于参数识别，我们提出了一种算法，计算，在每次迭代，正则化参数和模型参数。特别地，根据平衡原理更新正则化参数值，并且通过借助于非线性Gauss-Seidel方法求解相应的$L_1$正则化非线性最小二乘问题来获得模型参数值。我们分析了所提出的算法的收敛性能，并进行了广泛的测试合成和真实数据。一个Matlab软件，实现所提出的算法，可应要求提供给作者。
英文摘要：
Fast Field-Cycling Nuclear Magnetic Resonance relaxometry is a non-destructive technique to investigate molecular dynamics and structure of systems having a wide range of applications such as environment, biology, and food. Besides a considerable amount of literature about modeling and application of such technique in specific areas, an algorithmic approach to the related parameter identification problem is still lacking. We believe that a robust algorithmic approach will allow a unified treatment of different samples in several application areas. In this paper, we model the parameters identification problem as a constrained $L_1$-regularized non-linear least squares problem. Following the approach proposed in [Analytical Chemistry 2021 93 (24)], the non-linear least squares term imposes data consistency by decomposing the acquired relaxation profiles into relaxation contributions associated with 1H-1H and 1H-14N dipole-dipole interactions. The data fitting and the L1-based regularization terms are balanced by the so-called regularization parameter. For the parameters identification, we propose an algorithm that computes, at each iteration, both the regularization parameter and the model parameters. In particular, the regularization parameter value is updated according to a Balancing Principle and the model parameters values are obtained by solving the corresponding $L_1$-regularized non-linear least squares problem by means of the non-linear Gauss-Seidel method. We analyse the convergence properties of the proposed algorithm and run extensive testing on synthetic and real data. A Matlab software, implementing the presented algorithm, is available upon request to the authors.
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