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

arXiv: https://arxiv.org/abs/2604.15651 · HTML: https://mlsanity.com/paper/2604.15651/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 37 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Builds on (most cited first, 8 of 8)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements](https://mlsanity.com/paper/2111.12855/) (2021)
- [Deep Learning based Spectral CT Imaging](https://mlsanity.com/paper/2008.13570/) (2020)
- [Sparse2Inverse: Self-supervised inversion of sparse-view CT data](https://mlsanity.com/paper/2402.16921/) (2024)
- [Noisier2Inverse: Self-Supervised Learning for Image Reconstruction with Correlated Noise](https://mlsanity.com/paper/2503.19468/) (2025)
- [Equivariance2Inverse: A Practical Self-Supervised CT Reconstruction Method Benchmarked on Real, Limited-Angle, and Blurred Data](https://mlsanity.com/paper/2510.23317/) (2025)
- [Unsupervised denoising for sparse multi-spectral computed tomography](https://mlsanity.com/paper/2211.01159/) (2022)

## Abstract (arXiv)

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.