SPLIT: Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| author | Haltmeier, Markus Neumann, Lukas Gruber, Nadja Hwang, Gyeongha |
| author_facet | Haltmeier, Markus Neumann, Lukas Gruber, Nadja Hwang, Gyeongha |
| contents | Machine learning has achieved impressive performance in tomographic reconstruction, but supervised training requires paired measurements and ground-truth images that are often unavailable. This has motivated self-supervised approaches, which have primarily addressed denoising and, more recently, linear inverse problems. We address nonlinear inverse problems and introduce SPLIT (Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography), a self-supervised machine-learning framework for reconstructing images from nonlinear, incomplete, and noisy projection data without any samples of ground-truth images. SPLIT enforces cross-partition consistency and measurement-domain fidelity while exploiting complementary information across multiple partitions. Our main theoretical result shows that, under mild conditions, the proposed self-supervised objective is equivalent to its supervised counterpart in expectation. We regularize training with an automatic stopping rule that halts optimization when a no-reference image-quality surrogate saturates. As a concrete application, we derive SPLIT variants for multispectral computed tomography. Experiments on sparse-view acquisitions demonstrate high reconstruction quality and robustness to noise, surpassing classical iterative reconstruction and recent self-supervised baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15651 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | SPLIT: Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography Haltmeier, Markus Neumann, Lukas Gruber, Nadja Hwang, Gyeongha Computer Vision and Pattern Recognition 65R32, 44A12, 68T07 Machine learning has achieved impressive performance in tomographic reconstruction, but supervised training requires paired measurements and ground-truth images that are often unavailable. This has motivated self-supervised approaches, which have primarily addressed denoising and, more recently, linear inverse problems. We address nonlinear inverse problems and introduce SPLIT (Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography), a self-supervised machine-learning framework for reconstructing images from nonlinear, incomplete, and noisy projection data without any samples of ground-truth images. SPLIT enforces cross-partition consistency and measurement-domain fidelity while exploiting complementary information across multiple partitions. Our main theoretical result shows that, under mild conditions, the proposed self-supervised objective is equivalent to its supervised counterpart in expectation. We regularize training with an automatic stopping rule that halts optimization when a no-reference image-quality surrogate saturates. As a concrete application, we derive SPLIT variants for multispectral computed tomography. Experiments on sparse-view acquisitions demonstrate high reconstruction quality and robustness to noise, surpassing classical iterative reconstruction and recent self-supervised baselines. |
| title | SPLIT: Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography |
| topic | Computer Vision and Pattern Recognition 65R32, 44A12, 68T07 |
| url | https://arxiv.org/abs/2604.15651 |