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

TL;DR

SPLIT is a novel self-supervised framework for nonlinear tomographic image reconstruction that does not require ground-truth data, leveraging cross-partition consistency and measurement fidelity to outperform classical methods.

Contribution

It introduces SPLIT, a self-supervised learning method for nonlinear tomography that guarantees equivalence to supervised training under mild conditions and includes an automatic stopping rule.

Findings

SPLIT achieves high-quality reconstructions on sparse-view data.

It outperforms classical iterative and recent self-supervised methods.

Theoretical analysis shows equivalence to supervised objectives in expectation.

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.