L^1 data fitting for Inverse Problems yields optimal rates of convergence in case of discretized white Gaussian noise
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| Format: | Preprint |
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2025
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| _version_ | 1866918289706319872 |
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| author | Bätz, Kristina Werner, Frank |
| author_facet | Bätz, Kristina Werner, Frank |
| contents | It is well-known in practice, that L^1 data fitting leads to improved robustness compared to standard L^2 data fitting. However, it is unclear whether resulting algorithms will perform as well in case of regular data without outliers. In this paper, we therefore analyze generalized Tikhonov regularization with L^1 data fidelity for Inverse Problems F(u) = g in a general setting, including general measurement errors and errors in the forward operator. The derived results are then applied to the situation of discretized Gaussian white noise, and we show that the resulting error bounds allow for order-optimal rates of convergence. These findings are also investigated in numerical simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_11321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | L^1 data fitting for Inverse Problems yields optimal rates of convergence in case of discretized white Gaussian noise Bätz, Kristina Werner, Frank Numerical Analysis Primary 62G05, Secondary 65J22 It is well-known in practice, that L^1 data fitting leads to improved robustness compared to standard L^2 data fitting. However, it is unclear whether resulting algorithms will perform as well in case of regular data without outliers. In this paper, we therefore analyze generalized Tikhonov regularization with L^1 data fidelity for Inverse Problems F(u) = g in a general setting, including general measurement errors and errors in the forward operator. The derived results are then applied to the situation of discretized Gaussian white noise, and we show that the resulting error bounds allow for order-optimal rates of convergence. These findings are also investigated in numerical simulations. |
| title | L^1 data fitting for Inverse Problems yields optimal rates of convergence in case of discretized white Gaussian noise |
| topic | Numerical Analysis Primary 62G05, Secondary 65J22 |
| url | https://arxiv.org/abs/2511.11321 |