HyDRA: Hybrid Denoising Regularization for Measurement-Only DEQ Training

TL;DR

HyDRA introduces a measurement-only training framework for Deep Equilibrium models in image reconstruction, combining measurement consistency and denoising regularization, enabling effective reconstruction without supervised pairs.

Contribution

It proposes a novel measurement-only training method for DEQ models that integrates denoising regularization and adaptive early stopping, addressing data scarcity in image reconstruction.

Findings

Achieves competitive quality in sparse-view CT reconstruction.

Enables fast inference with measurement-only training.

Demonstrates effectiveness without supervised training data.

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.