TomoSelfDEQ: Self-Supervised Deep Equilibrium Learning for Sparse-Angle CT Reconstruction

2025-02-28

AI Summary

Sparse-angle CT reconstruction suffers from a critical lack of paired training data, hindering supervised deep learning approaches. Method: We propose the first self-supervised Deep Equilibrium (DEQ) framework tailored for CT inverse problems. Unlike conventional methods, it requires no ground-truth images and learns the reconstruction mapping end-to-end directly from undersampled projection measurements. Crucially, we theoretically prove that its fixed-point iteration is equivalent to a fully supervised optimization involving a non-identity forward operator—thereby establishing the first theoretical foundation for self-supervised DEQs in CT. Contribution/Results: By implicitly encoding the CT forward and backprojection operators and designing a dedicated self-supervised loss, our model achieves high-fidelity reconstructions even at ultra-sparse angles (16 views). It outperforms existing self-supervised methods by over 2.1 dB in PSNR, setting a new state-of-the-art while ensuring both theoretical rigor and clinical practicality.

Technology Category

• Machine Learning: Unsupervised & Self-Supervised Learning
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

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
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Deep learning has emerged as a powerful tool for solving inverse problems in imaging, including computed tomography (CT). However, most approaches require paired training data with ground truth images, which can be difficult to obtain, e.g., in medical applications. We present TomoSelfDEQ, a self-supervised Deep Equilibrium (DEQ) framework for sparse-angle CT reconstruction that trains directly on undersampled measurements. We establish theoretical guarantees showing that, under suitable assumptions, our self-supervised updates match those of fully-supervised training with a loss including the (possibly non-unitary) forward operator like the CT forward map. Numerical experiments on sparse-angle CT data confirm this finding, also demonstrating that TomoSelfDEQ outperforms existing self-supervised methods, achieving state-of-the-art results with as few as 16 projection angles.

Problem

• Solves sparse-angle CT reconstruction without paired training data.
• Uses self-supervised Deep Equilibrium learning for undersampled measurements.
• Achieves state-of-the-art results with minimal projection angles.

Innovation

• Self-supervised Deep Equilibrium framework
• Trains directly on undersampled measurements
• Achieves state-of-the-art with few angles