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arXiv · 2601.01228

HyDRA: Hybrid Denoising Regularization for Measurement-Only DEQ Training

Markus Haltmeier·Lukas Neumann·Nadja Gruber·Johannes Schwab·Gyeongha Hwang
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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.

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Markus Haltmeier, Lukas Neumann, Nadja Gruber, Johannes Schwab, Gyeongha Hwang. 2026-01-03. HyDRA: Hybrid Denoising Regularization for Measurement-Only DEQ Training. https://arxiv.org/abs/2601.01228

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