Scalable Unrolled Chains for MRI Reconstruction

Fully sampled MRI requires dense k-space acquisition, leading to long scan times, reduced clinical throughput, and increased sensitivity to patient motion. Accelerated MRI addresses this by acquiring undersampled k-space data and reconstructing the missing information computationally. However, reconstruction from undersampled measurements is highly ill-posed and can introduce aliasing artifacts, noise amplification, and loss of anatomical detail. Although conventional parallel imaging and compressed sensing methods mitigate these issues, and deep learning methods have further improved reconstruction quality, preserving high-frequency structures under aggressive undersampling remains challenging. In this work, we propose a Variational Network with a Wavelet-based U-Net (W-UNet) for accelerated MRI reconstruction. The framework combines physics-guided iterative reconstruction with learnable multi-scale frequency representations. Standard pooling operations are replaced with Discrete Wavelet Transform and Inverse Wavelet Transform modules, enabling lossless downsampling while preserving low-frequency structure and high-frequency edge details. Integrated into the refinement and sensitivity map estimation stages, the proposed design improves artifact suppression, feature preservation, and reconstruction fidelity in both single-coil and multi-coil settings. Experiments on fastMRI knee and M4Raw brain datasets show state-of-the-art performance. Ablation studies further confirm the effectiveness of wavelet-based feature decomposition for accelerated MRI reconstruction.

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.

MRI provides excellent soft-tissue contrast without ionizing radiation, but long acquisition times increase patient discomfort while also raising exam costs and limiting scanner throughput. A common approach to reduce scan time is to acquire fewer measurements, which yields an ill-posed linear inverse problem; recovering diagnostic-quality images therefore requires incorporating prior knowledge beyond the measured data. In follow-up exams, the most recent prior scan of a patient can provide a highly informative subject-specific context, but practical use is complicated by temporal changes (including pathology progression), misalignment between scans, and protocol drift across acquisitions. In this work, we introduce L-TGVN, a Longitudinal Trust-Guided Variational Network that leverages prior scans as side information to reconstruct the current scan from heavily undersampled measurements. Crucially, L-TGVN constrains the influence of prior scans to be consistent with the acquired measurements. Unlike many existing longitudinal reconstruction methods, it does not require explicit pre-registration between prior and current scans. It further accommodates differences in acquisition protocols across visits (e.g., changes in sequence parameters). We evaluate L-TGVN against matched-capacity baselines, including prior-guided methods and methods that do not use longitudinal priors, and observe consistent improvements in standard quantitative metrics together with better preservation of fine structures at challenging accelerations. Source code is available at github.com/sodicksonlab/L-TGVN.