Exponential relaxation data analysis by parametrized regularization of severely ill-posed Fredholm integral equations of the first kind
Numerical Analysis
2023-09-12 v3 Numerical Analysis
Abstract
This paper presents a novel approach to construct regularizing operators for severely ill-posed Fredholm integral equations of the first kind by introducing parametrized discretization. The optimal values of discretization and regularization parameters are computed simultaneously by solving a minimization problem formulated based on a regularization parameter search criterion. The effectiveness of the proposed approach is demonstrated through examples of noisy Laplace transform inversions and the deconvolution of nuclear magnetic resonance relaxation data.
Keywords
Cite
@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}
}
Comments
This version clarifies the main point of previous manuscript. The paper has been completely rewritten: new title, new figures, more sections