Deep Unrolled Networks in Representation Space Applied to MRI Reconstruction

2026-06-19

AI Summary

This work addresses the limitation of existing deep unrolling networks, which rely on heuristic data consistency terms in the representation space and thus fail to strictly enforce physical measurement constraints, compromising reconstruction fidelity. To overcome this, the authors propose DUNE—a novel framework that, for the first time, integrates learnable regularization with an explicit physical forward model directly in the representation space. By leveraging vector-Jacobian products (VJPs), DUNE enables exact gradient backpropagation through the data consistency term via the chain rule, guaranteeing that reconstructed images rigorously adhere to observed measurements. The approach is compatible with diverse backbone architectures and supports iterative refinement guided by pretrained encoders. Extensive experiments on both single-coil portable low-field and multi-coil clinical high-field accelerated MRI demonstrate that DUNE consistently outperforms state-of-the-art methods, achieving superior image quality and structural fidelity.

Abstract

Deep unrolled networks (DUNs) integrate physical forward models with learned regularization in cascaded network architectures, achieving exceptional performance in inverse problems while maintaining interpretability. While most DUNs operate in the object domain (e.g., image space), recent variants explored representation spaces for improved information flow. However, these methods rely on heuristic methods for data consistency (DC), sacrificing fidelity with measurements. In this work, we introduce DUNE (Deep Unrolled Networks in rEpresentation space), a framework that maintains exact adherence to physical measurements while operating in learned representation spaces. By deriving the DC gradient via the chain rule and implementing it through the Vector-Jacobian Product (VJP), we enable exact backpropagation of measurement residuals into the representation space. This formulation supports diverse architectural backbones, including pre-trained encoders to guide the iterative process. We assess DUNE against state-of-the-art baselines on accelerated MRI reconstruction tasks, demonstrating that exact VJP-based gradients yield superior reconstruction quality and structural fidelity across both single-channel portable low-field and multi-channel clinical high-field MRI acquisitions. The code will be available upon publication at https://github.com/EfeIlicak/DUNE.

Problem

• MRI reconstruction
• data consistency
• representation space
• inverse problems
• deep unrolled networks

Innovation

• Deep Unrolled Networks
• Representation Space
• Vector-Jacobian Product
• Data Consistency
• MRI Reconstruction