Stochastic asymptotical regularization for nonlinear ill-posed problems
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916369031757824 |
|---|---|
| author | Long, Haie Zhang, Ye |
| author_facet | Long, Haie Zhang, Ye |
| contents | Recently, the stochastic asymptotical regularization (SAR) has been developed in (\emph{Inverse Problems}, 39: 015007, 2023) for the uncertainty quantification of the stable approximate solution of linear ill-posed inverse problems. In this paper, we extend the regularization theory of SAR for nonlinear inverse problems. By combining techniques from classical regularization theory and stochastic analysis, we prove the regularizing properties of SAR with regard to mean-square convergence. The convergence rate results under the canonical sourcewise condition are also studied. Several numerical examples are used to show the accuracy and advantages of SAR: compared with the conventional deterministic regularization approaches for deterministic inverse problems, SAR can quantify the uncertainty in error estimates for ill-posed problems, improve accuracy by selecting the optimal path, escape local minima for nonlinear problems, and identify multiple solutions by clustering samples of obtained approximate solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_07162 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stochastic asymptotical regularization for nonlinear ill-posed problems Long, Haie Zhang, Ye Numerical Analysis Recently, the stochastic asymptotical regularization (SAR) has been developed in (\emph{Inverse Problems}, 39: 015007, 2023) for the uncertainty quantification of the stable approximate solution of linear ill-posed inverse problems. In this paper, we extend the regularization theory of SAR for nonlinear inverse problems. By combining techniques from classical regularization theory and stochastic analysis, we prove the regularizing properties of SAR with regard to mean-square convergence. The convergence rate results under the canonical sourcewise condition are also studied. Several numerical examples are used to show the accuracy and advantages of SAR: compared with the conventional deterministic regularization approaches for deterministic inverse problems, SAR can quantify the uncertainty in error estimates for ill-posed problems, improve accuracy by selecting the optimal path, escape local minima for nonlinear problems, and identify multiple solutions by clustering samples of obtained approximate solutions. |
| title | Stochastic asymptotical regularization for nonlinear ill-posed problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2211.07162 |