# Deep Unrolled Networks in Representation Space Applied to MRI Reconstruction

arXiv: https://arxiv.org/abs/2606.21602 · HTML: https://mlsanity.com/paper/2606.21602/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 19 Jun 2026.

## Builds on (most cited first, 8 of 8)

- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [DuDoRNet: Learning a Dual-Domain Recurrent Network for Fast MRI Reconstruction with Deep T1 Prior](https://mlsanity.com/paper/2001.03799/) (2020)
- [Physics-/Model-Based and Data-Driven Methods for Low-Dose Computed Tomography: A survey](https://mlsanity.com/paper/2203.15725/) (2022)
- [DEQ-MPI: A Deep Equilibrium Reconstruction with Learned Consistency for Magnetic Particle Imaging](https://mlsanity.com/paper/2212.13233/) (2022)
- [A Tutorial on MRI Reconstruction: From Modern Methods to Clinical Implications](https://mlsanity.com/paper/2507.16715/) (2025)
- [Deep Unfolded Recovery of Sub-Nyquist Sampled Ultrasound Image](https://mlsanity.com/paper/2103.01263/) (2021)

## Abstract (arXiv)

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.