Exponential relaxation data analysis by parametrized regularization of severely ill-posed Fredholm integral equations of the first kind

Vladimir V Kryzhniy

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arXiv · 2307.05878

Exponential relaxation data analysis by parametrized regularization of severely ill-posed Fredholm integral equations of the first kind

Vladimir V Kryzhniy

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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.

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Vladimir V Kryzhniy. 2023-07-12. Exponential relaxation data analysis by parametrized regularization of severely ill-posed Fredholm integral equations of the first kind. https://arxiv.org/abs/2307.05878

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