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

2026-04-16

AI Summary

This work addresses the challenge of self-supervised reconstruction in nonlinear tomography, where ground-truth image labels are unavailable. It proposes SPLIT, a framework that partitions measurement data and leverages cross-partition consistency constraints, measurement-domain fidelity, and an automatic early-stopping mechanism driven by no-reference image quality metrics to achieve high-quality reconstructions without supervision from ground-truth images. SPLIT represents the first effective extension of self-supervised learning to nonlinear inverse problems and theoretically demonstrates that its objective function is equivalent in expectation to that of supervised methods. In sparse-view multispectral CT experiments, SPLIT significantly outperforms conventional iterative algorithms and existing self-supervised baselines, while exhibiting strong robustness to noise.

Technology Category

• Machine Learning: Unsupervised & Self-Supervised Learning
• Computer Vision: Segmentation
• Search and Optimization: Non-convex Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• nonlinear tomography
• self-supervised learning
• inverse problems
• image reconstruction
• no ground-truth

Innovation

• self-supervised learning
• nonlinear tomography
• image reconstruction
• cross-partition consistency
• inverse problems