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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.17465 |
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| _version_ | 1866909654632628224 |
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| author | Kirisits, Clemens Mejri, Bochra Pereverzev, Sergei Scherzer, Otmar Shi, Cong |
| author_facet | Kirisits, Clemens Mejri, Bochra Pereverzev, Sergei Scherzer, Otmar Shi, Cong |
| contents | The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior experiments. This approach enables the integration of data-driven insights into the solution of inverse problems governed by physical models. \emph{Inverse problems}, in general, aim to uncover the \emph{inner mechanisms} of an observed system based on indirect or incomplete measurements. This field has far-reaching applications across various disciplines, such as medical or geophysical imaging, as well as, more broadly speaking, industrial processes where identifying hidden parameters is essential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17465 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularization of Nonlinear Inverse Problems -- From Functional Analysis to Data-Driven Approaches Kirisits, Clemens Mejri, Bochra Pereverzev, Sergei Scherzer, Otmar Shi, Cong Optimization and Control 47A52, 65-02, 34A55, 65L09, 65N21, 65T60 The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior experiments. This approach enables the integration of data-driven insights into the solution of inverse problems governed by physical models. \emph{Inverse problems}, in general, aim to uncover the \emph{inner mechanisms} of an observed system based on indirect or incomplete measurements. This field has far-reaching applications across various disciplines, such as medical or geophysical imaging, as well as, more broadly speaking, industrial processes where identifying hidden parameters is essential. |
| title | Regularization of Nonlinear Inverse Problems -- From Functional Analysis to Data-Driven Approaches |
| topic | Optimization and Control 47A52, 65-02, 34A55, 65L09, 65N21, 65T60 |
| url | https://arxiv.org/abs/2506.17465 |