Learned Regularization for Inverse Problems: Insights from a Spectral Model
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909216221954048 |
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| author | Burger, Martin Kabri, Samira |
| author_facet | Burger, Martin Kabri, Samira |
| contents | In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization methods and their convergence in terms of the underlying data distributions, which paves the way for future theoretical studies. Based on a simple spectral learning model previously introduced for supervised learning, we investigate some key properties of different learning paradigms for inverse problems, which can be formulated independently of specific architectures. In particular we investigate the regularization properties, bias, and critical dependence on training data distributions. Moreover, our framework allows to highlight and compare the specific behavior of the different paradigms in the infinite-dimensional limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09845 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Learned Regularization for Inverse Problems: Insights from a Spectral Model Burger, Martin Kabri, Samira Numerical Analysis Machine Learning 47A52, 65J22, 68T05 In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization methods and their convergence in terms of the underlying data distributions, which paves the way for future theoretical studies. Based on a simple spectral learning model previously introduced for supervised learning, we investigate some key properties of different learning paradigms for inverse problems, which can be formulated independently of specific architectures. In particular we investigate the regularization properties, bias, and critical dependence on training data distributions. Moreover, our framework allows to highlight and compare the specific behavior of the different paradigms in the infinite-dimensional limit. |
| title | Learned Regularization for Inverse Problems: Insights from a Spectral Model |
| topic | Numerical Analysis Machine Learning 47A52, 65J22, 68T05 |
| url | https://arxiv.org/abs/2312.09845 |