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Data-driven stochastic asymptotic regularization for ill-posed inverse problems with a posteriori and heuristic stopping — arXiv:2610.38279

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.38279
License (as archived): CC0-1.0
Archived: 2026-11-01T02:35:35.831Z
SHA-256 of the archived text: 081146a7a54c1cb2fea8702d9d5d42ada0790361bff48f136592a1d580dcacc1
Stable URL of this page: https://metraipolis.com/documento/dc_4bb3757bb13f

How to cite

Data-driven stochastic asymptotic regularization for ill-posed inverse problems with a posteriori and heuristic stopping — arXiv:2610.38279 — arXiv (en), https://arxiv.org/abs/2610.38279 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_4bb3757bb13f (Metraipolis archive dc_4bb3757bb13f, sha256 081146a7a54c1cb2fea8702d9d5d42ada0790361bff48f136592a1d580dcacc1)

BibTeX

@misc{dc4bb3757bb13f,
  title = {Data-driven stochastic asymptotic regularization for ill-posed inverse problems with a posteriori and heuristic stopping — arXiv:2610.38279},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.38279},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_4bb3757bb13f; sha256 081146a7a54c1cb2fea8702d9d5d42ada0790361bff48f136592a1d580dcacc1},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.38279. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A novel Data-driven STochastic Asymptotic Regularization (\texttt{D-STAR}) method is proposed for solving linear and nonlinear ill-posed inverse problems, which incorporates a data-driven drift and a stochastic diffusion mechanism. Both known and unknown noise level cases are accommodated by the method, thereby making the framework applicable to a broader range of practical inverse problems. For known noise level, a modified discrepancy principle is employed, whereas for unknown noise level, a heuristic stopping rule based solely on noisy data is developed. For each stopping rule, an appropriate diffusion term is defined and the well-posedness of the associated stochastic differential equation is demonstrated. The finite termination of \texttt{D-STAR} method under both stopping rules is established and its convergence to the exact solution in the noise-free setting is proved. For the noisy data, stability and the regularization property in the mean-square sense are further established. In addition, the uncertainty quantification of the proposed method and its comparison with the Stochastic Asymptotic Regularization (\texttt{SAR}) method under both rules are provided. Furthermore, it is shown that local minima arising in the Data-Driven Iteratively Regularized Landweber (\texttt{DDIRLI}) method may be escaped. Finally, detailed numerical experiments, including comparisons with existing \texttt{DDIRLI} and \texttt{SAR} methods, are presented on X-ray computed tomography and nonlinear schlieren tomography for both stopping rules, thereby demonstrating the performance of \texttt{D-STAR}.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Numerical Analysis (math.NA) ; Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2610.38279 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-01T02:14:58.660Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).