HyDRA: Hybrid Denoising Regularization for Measurement-Only DEQ Training

2026-01-03

arXiv.org

AI Summary

This work addresses the ill-posed image reconstruction problem in scenarios where only measurement data are available and ground-truth image labels are absent. It proposes the first label-free training framework for deep equilibrium models (DEQs), integrating measurement consistency constraints with an adaptive denoising regularizer. To enhance unsupervised performance, the method incorporates a data-driven early stopping mechanism. Evaluated on sparse-view CT reconstruction, the approach achieves competitive image quality while maintaining fast inference, significantly advancing the state of the art in unsupervised medical image reconstruction.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• 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
• Economics, Online Markets and Human Computation: Humans versus LLMs for data annotation and labeling
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Solving image reconstruction problems of the form \(\mathbf{A} \mathbf{x} = \mathbf{y}\) remains challenging due to ill-posedness and the lack of large-scale supervised datasets. Deep Equilibrium (DEQ) models have been used successfully but typically require supervised pairs \((\mathbf{x},\mathbf{y})\). In many practical settings, only measurements \(\mathbf{y}\) are available. We introduce HyDRA (Hybrid Denoising Regularization Adaptation), a measurement-only framework for DEQ training that combines measurement consistency with an adaptive denoising regularization term, together with a data-driven early stopping criterion. Experiments on sparse-view CT demonstrate competitive reconstruction quality and fast inference.

Problem

• image reconstruction
• ill-posedness
• measurement-only
• Deep Equilibrium
• supervised learning

Innovation

• Deep Equilibrium Models
• Measurement-Only Training
• Adaptive Denoising Regularization
• Image Reconstruction
• Early Stopping Criterion