Efficient TV regularization of large-scale linear inverse problems via the SCD semismooth* Newton method with applications in tomography
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909036028362752 |
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| author | Gfrerer, Helmut Hubmer, Simon Kindermann, Stefan Kultima, Jaakko Ramlau, Ronny Tarvainen, Tanja |
| author_facet | Gfrerer, Helmut Hubmer, Simon Kindermann, Stefan Kultima, Jaakko Ramlau, Ronny Tarvainen, Tanja |
| contents | In this paper, we consider the efficient numerical minimization of Tikhonov functionals resulting from total-variation (TV) regularization of linear inverse problems. Since the TV penalty is non-smooth, this is typically done either via smooth approximations, which are inexact, or using non-smooth optimization techniques, which can often be numerically expensive, in particular for large-scale problems. Here, we present a numerically efficient minimization approach based on the recently proposed semismooth* Newton method, which employs a novel concept of graphical derivatives and exhibits locally superlinear convergence. The proposed approach is specifically tailored to TV regularization, suitable for large-scale inverse problems, and supported by strong mathematical convergence guarantees. Furthermore, we demonstrate its performance on two (large-scale) tomographic imaging problems and compare our results to those obtained via other state-of-the-art TV regularization approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12041 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient TV regularization of large-scale linear inverse problems via the SCD semismooth* Newton method with applications in tomography Gfrerer, Helmut Hubmer, Simon Kindermann, Stefan Kultima, Jaakko Ramlau, Ronny Tarvainen, Tanja Numerical Analysis In this paper, we consider the efficient numerical minimization of Tikhonov functionals resulting from total-variation (TV) regularization of linear inverse problems. Since the TV penalty is non-smooth, this is typically done either via smooth approximations, which are inexact, or using non-smooth optimization techniques, which can often be numerically expensive, in particular for large-scale problems. Here, we present a numerically efficient minimization approach based on the recently proposed semismooth* Newton method, which employs a novel concept of graphical derivatives and exhibits locally superlinear convergence. The proposed approach is specifically tailored to TV regularization, suitable for large-scale inverse problems, and supported by strong mathematical convergence guarantees. Furthermore, we demonstrate its performance on two (large-scale) tomographic imaging problems and compare our results to those obtained via other state-of-the-art TV regularization approaches. |
| title | Efficient TV regularization of large-scale linear inverse problems via the SCD semismooth* Newton method with applications in tomography |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2605.12041 |