Unrolled Neural Networks

Background and purpose: We propose PGPI4MR (prior-guided, physics-informed 4D MRI reconstruction), a deep learning method that leverages information from other respiratory phases or a setup scan, the first 30 s of the same scan, to improve 4D MRI reconstruction without extra scan time. Materials and methods: PGPI4MR is an unrolled network that reconstructs 16 respiratory phases from 60, 30, or 15 s of data, and single 3D volumes, each from 0.29-0.49 s of data, using a setup-scan image. The networks were trained once, on other volunteers, and were not retrained for new volunteers. We evaluated PGPI4MR on measured k-space from three datasets: free-breathing MR-linac (1.5T) and abdominal (3T) scans, and thigh scans with cuff compression (1.5T). All methods, including comparative models, received identical samples and were scored similarly. Results: In vivo, PGPI4MR had the lowest held-out error for 4D MRI at every scan time, and its 16 phases were ready a median of 7.5-13 s after the scan on the 2 GPUs tested. Coupling the 16 respiratory phases reduced the error at 60 s by 9.1% compared with reconstructing each phase alone. For sub-second MRI, the error at 0.49 s was 15.5% lower than that of the best comparison method, classical reconstruction toward the same prior, and on the faster GPU, every 0.29 s window was acquired and reconstructed within 0.5 s. Without retraining, PGPI4MR matched the best methods on the 3T abdominal scans but not on the thigh scans; after retraining on thigh data, it reduced the held-out error by 6.6% relative to the best comparison method. Conclusion: Prior information allowed PGPI4MR to reconstruct 4D and sub-second MRI more accurately than compressed sensing and a published 4D network, within seconds and without extra scan time. This could support 4D MRI for treatment planning and 3D motion monitoring during MR-guided radiotherapy.

Unrolled variational networks achieve state-of-the-art performance for accelerated MRI reconstruction, but standard end-to-end training becomes prohibitively memory intensive as the number and width of cascades increase. We propose a memory-efficient training framework that updates a randomly sampled cascade while retaining supervision from the final reconstruction loss. The error signal is propagated from the end of the chain to the sampled cascade using an activation-light backward pass that avoids storing full chain activations, thereby decoupling training memory from chain length. A time-conditioned network shared across cascades further keeps the parameter count independent of chain length. The backward pass is approximate only through frozen normalization statistics, and a trained exact gradient control shows the approximation leaves reconstruction quality unchanged. The framework remains trainable at chain lengths and cascade widths where standard end-to-end backpropagation exhausts GPU memory. On fastMRI single-coil knee and multi-coil brain reconstruction, our method consistently outperforms other local training approaches. On high-SNR knee slices, our method surpasses E2E-VarNet at $8\times$ and matches it at $4\times$, while on the complete brain validation set it surpasses E2E-VarNet at $8\times$ and achieves comparable performance at $4\times$, with fewer parameters, lower peak memory, and faster per-iteration training. Code is available at https://github.com/emehillaj/scalable-unrolled-mri.

Metal implants corrupt MRI measurements throughout $k$-space, yet existing accelerated MRI methods assume clean data and most metal artifact reduction approaches assume fully sampled acquisitions. No public dataset provides paired $k$-space and images with and without metal for the same anatomy, and no framework jointly addresses artifact-aware acquisition and reconstruction across sampling trajectories. We present OpenMASC, an open-source pipeline covering the full workflow from data generation to deployment. A physics-based data generation module converts public CT volumes into paired clean and metal-corrupted MRI data in both Cartesian and radial formats. MA-VarNet, an unrolled reconstruction network with a per-cascade DC Rectifier, corrects artifacts that data-consistency steps reintroduce from corrupted measurements. A reinforcement learning agent actively selects $k$-space readouts and co-trains with the reconstruction network through a decoupled three-stage procedure. The framework is trajectory-agnostic except for the data-consistency operator, supporting both Cartesian and radial acquisition without architectural changes. Experiments on two datasets at $4\times$ and $8\times$ acceleration demonstrate consistent improvements over conventional and learned baselines on both trajectories.

We present FlowMoDL, an unrolled neural network for highly accelerated 4D flow MRI reconstruction that directly optimizes for both anatomical magnitude and phase-derived velocity accuracy. Building on the MoDL framework, FlowMoDL alternates a learned (3+1)D spatiotemporal denoiser with conjugate-gradient data-consistency updates based on the SENSE forward model. A novel dual-pathway conditioning scheme adapts the denoiser features and data-consistency weighting, enabling a single model to handle varying acceleration factors ($10\times$ to $50\times$). To ensure physiological accuracy, the network is trained using a deep-supervision composite loss that explicitly penalizes velocity magnitude and angular errors, stabilized by a curriculum schedule. We evaluate FlowMoDL on the multi-center CMRx4DFlow dataset against classical and deep-learning baselines (CG-SENSE, MoDL, FlowVN, and FlowMRI-Net). A key advantage of FlowMoDL is its superior gradient step efficiency. When evaluated under an equivalent, limited budget of gradient steps, competing flow-specific networks degrade significantly. In contrast, FlowMoDL robustly converges and strictly outperforms all competitors across all acceleration factors in magnitude SSIM, nRMSE, relative velocity error, and angular error, successfully recovering sharp structural details and temporally coherent velocity fields.

Conventional cardiac cine MRI relies on breath-hold Cartesian acquisitions, which are vulnerable to motion artifacts and can be uncomfortable or infeasible, particularly for pediatric and other noncompliant patients who cannot reliably hold their breath. Free-breathing radial acquisitions can alleviate these limitations, but robust reconstruction at high acceleration remains challenging due to prominent streak artifacts. To address these limitations, we propose Cine-DL, a clinically oriented framework that couples targeted k-space preprocessing with fast, model-based deep reconstruction. In this pipeline, raw free-breathing radial data undergo retrospective cardiac binning and respiratory gating to resolve cardiac phases and discard motion-corrupted spokes. We then introduce Streak Optimized Coil Compression (SOC), which explicitly preserves cardiac signals while suppressing peripheral interference that typically drives the streak artifacts. The resulting 2D+t cine series is reconstructed with an unrolled network that alternates a ResNet proximal operator with physics-based data consistency updates solved via conjugate gradient. We further employ a memory-efficient training strategy that reduces peak memory usage. We evaluate Cine-DL on free-breathing volunteer data against established baselines (k-t SENSE and iGRASP) and demonstrate clinical translation via hospital deployment on newly acquired patient data. Our experiments show that Cine-DL consistently improves quantitative metrics and visual fidelity, supporting a practical route toward routine, time-sensitive clinical adoption of free-breathing cine MRI.

The emergence of large-scale pretrained foundation models has transformed computer vision, enabling strong performance across diverse downstream tasks. However, their potential for physics-based inverse problems, such as accelerated cardiac MRI reconstruction, remains largely underexplored. In this work, we investigate whether natural-domain foundation models can serve as effective image priors for accelerated cardiac MRI reconstruction, and compare the performance obtained against domain-specific counterparts such as BiomedCLIP. We propose an unrolled reconstruction framework that incorporates pretrained, frozen visual encoders, such as CLIP, DINOv2, and BiomedCLIP, within each cascade to guide the reconstruction process. Through extensive experiments, we show that while task-specific state-of-the-art reconstruction models such as E2E-VarNet achieve superior performance in standard in-distribution settings, foundation-model-based approaches remain competitive. More importantly, in challenging cross-domain scenarios, where models are trained on cardiac MRI and evaluated on anatomically distinct knee and brain datasets--foundation models exhibit improved robustness, particularly under high acceleration factors and limited low-frequency sampling. We further observe that natural-image-pretrained models, such as CLIP, learn highly transferable structural representations, while domain-specific pretraining (BiomedCLIP) provides modest additional gains in more ill-posed regimes. Overall, our results suggest that pretrained foundation models offer a promising source of transferable priors, enabling improved robustness and generalization in accelerated MRI reconstruction.

Machine learning models often struggle to generalize across domains with varying data distributions, such as differing noise levels, leading to degraded performance. Traditional strategies like personalized training, which trains separate models per domain, and joint training, which uses a single model for all domains, have significant limitations in flexibility and effectiveness. To address this, we propose two novel domain adaptation methods for regression tasks based on interpretable unrolled networks--deep architectures inspired by iterative optimization algorithms. These models leverage the functional dependence of select tunable parameters on domain variables, enabling controlled adaptation during inference. Our methods include Parametric Tunable-Domain Adaptation (P-TDA), which uses known domain parameters for dynamic tuning, and Data-Driven Tunable-Domain Adaptation (DD-TDA), which infers domain adaptation directly from input data. We validate our approach on compressed sensing problems involving noise-adaptive sparse signal recovery, domain-adaptive gain calibration, and domain-adaptive phase retrieval, demonstrating improved or comparable performance to domain-specific models while surpassing joint training baselines. This work highlights the potential of unrolled networks for effective, interpretable domain adaptation in regression settings.

Deep unrolled models (DUM) have become the state-of-the-art for accelerated MRI reconstruction, yet their robustness under domain shift remains a critical barrier to clinical adoption. In this work, we identify coil sensitivity map (CSM) estimation as the primary bottleneck limiting generalization. To address this, we propose UEPS, a novel DUM architecture featuring three key designs: (i) an Unrolled Expanded (UE) design that eliminates CSM dependency by reconstructing each coil independently; (ii) progressive resolution, which leverages k-space-to-image mapping for efficient coarse-to-fine refinement; and (iii) sparse attention tailored to MRI's 1D undersampling nature. These physics-grounded designs enable gains in robustness and computational efficiency. We construct a large-scale zero-shot transfer benchmark comprising 10 out-of-distribution (OOD) test sets spanning diverse clinical shifts, anatomy, view, contrast, vendor, field strength, and coil configurations. Extensive experiments demonstrate that UEPS consistently and substantially outperforms existing DUM, end-to-end, diffusion, and untrained methods across all OOD tests, achieving state-of-the-art robustness with low-latency inference suitable for real-time deployment.

Accelerated 3D late gadolinium enhancement (LGE) MRI requires robust reconstruction methods to recover thin atrial structures from undersampled k-space data. While unrolled model-based networks effectively integrate physics-driven data consistency with learned priors, they operate at the acquired resolution and may fail to fully recover high-frequency detail. We propose a hybrid unrolled reconstruction framework in which an Enhanced Deep Super-Resolution (EDSR) network replaces the proximal operator within each iteration of the optimization loop, enabling joint super-resolution enhancement and data consistency enforcement. The model is trained end-to-end on retrospectively undersampled preclinical 3D LGE datasets and compared against compressed sensing, Model-Based Deep Learning (MoDL), and self-guided Deep Image Prior (DIP) baselines. Across acceleration factors, the proposed method consistently improves PSNR and SSIM over standard unrolled reconstruction and better preserves fine cardiac structures, leading to improved LA (left atrium) segmentation performance. These results demonstrate that integrating super-resolution priors directly within model-based reconstruction provides measurable gains in accelerated 3D LGE MRI.