基于参数化正则化的严重病态第一类 Fredholm 积分方程的指数弛豫数据分析
数值分析
2023-09-12 v3 数值分析
摘要
本文提出一种通过引入参数化离散化来构造严重病态第一类 Fredholm 积分方程正则化算子的新方法。离散化与正则化参数的最优值通过求解基于正则化参数搜索准则所构造的最小化问题同时算出。所提方法的有效性通过含噪拉普拉斯变换反演以及核磁共振弛豫数据反卷积的实例得以验证。
引用
@article{arxiv.2307.05878,
title = {Exponential relaxation data analysis by parametrized regularization of severely ill-posed Fredholm integral equations of the first kind},
author = {Vladimir V Kryzhniy},
journal= {arXiv preprint arXiv:2307.05878},
year = {2023}
}
备注
This version clarifies the main point of previous manuscript. The paper has been completely rewritten: new title, new figures, more sections