Ensemble Kalman inversion with non-smooth regularization
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914414449393664 |
|---|---|
| author | Weissmann, Simon |
| author_facet | Weissmann, Simon |
| contents | This paper investigates ensemble Kalman inversion (EKI) for variational inverse problems with convex, potentially non-smooth regularization. While deterministic EKI and its Tikhonov-regularized variants have primarily been analyzed for smooth objectives, a corresponding framework accommodating subgradient dynamics has not yet been established. To address this gap, we introduce a subgradient-based formulation of EKI (SEKI) that incorporates non-smooth regularizers through a covariance-preconditioned differential inclusion for the ensemble mean. In the linear forward-model setting, well-posedness of the resulting continuous-time particle system is established under minimal assumptions on the regularization functional using maximal monotone operator theory and Yosida approximations. Motivated by the continuous-time dynamics, we propose an explicit discrete-time scheme that preserves the derivative-free structure of EKI and analyze its convergence as an optimization method in the strongly convex case. Numerical experiments in computed tomography with total variation regularization and sparse recovery with $\ell_1$ penalties illustrate that non-smooth regularization can be incorporated into ensemble Kalman inversion in a stable and principled manner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21916 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ensemble Kalman inversion with non-smooth regularization Weissmann, Simon Numerical Analysis Optimization and Control This paper investigates ensemble Kalman inversion (EKI) for variational inverse problems with convex, potentially non-smooth regularization. While deterministic EKI and its Tikhonov-regularized variants have primarily been analyzed for smooth objectives, a corresponding framework accommodating subgradient dynamics has not yet been established. To address this gap, we introduce a subgradient-based formulation of EKI (SEKI) that incorporates non-smooth regularizers through a covariance-preconditioned differential inclusion for the ensemble mean. In the linear forward-model setting, well-posedness of the resulting continuous-time particle system is established under minimal assumptions on the regularization functional using maximal monotone operator theory and Yosida approximations. Motivated by the continuous-time dynamics, we propose an explicit discrete-time scheme that preserves the derivative-free structure of EKI and analyze its convergence as an optimization method in the strongly convex case. Numerical experiments in computed tomography with total variation regularization and sparse recovery with $\ell_1$ penalties illustrate that non-smooth regularization can be incorporated into ensemble Kalman inversion in a stable and principled manner. |
| title | Ensemble Kalman inversion with non-smooth regularization |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2603.21916 |