SPLIT: Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography

• URL: http://arxiv.org/abs/2604.15651v1
• Date: Fri, 17 Apr 2026 02:47:54 GMT
• Title: SPLIT: Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography
• Abstract summary: We introduce SPLIT (Self-supervised Partitioning for Learned Inversion in Tomography), a self-supervised machine-learning framework for reconstructing images from nonlinear, incomplete, and noisy projection data without any samples of ground-truth images.<n>Our main theoretical result shows that, under mild conditions, the proposed self-supervised objective is equivalent to its supervised counterpart in expectation.<n> Experiments on sparse-view robustness demonstrate high reconstruction quality and saturate to noise, surpassing classical iterative reconstruction and recent self-supervised baselines.
• Score: 2.5743491116216037
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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