Accelerated MR Elastography Using Learned Neural Network Representation
Authors: Xi Peng
Organizations: Departments of Radiology, Biomedical Engineering, Electronic and Computer Engineering, and Mechanical Engineering, University of Iowa, Iowa City, IA 52246 · Department of Radiology, University of Iowa, Iowa City, IA, 52246
Abstract
To develop a deep-learning method for achieving fast high-resolution MR elastography from highly undersampled data without the need of high-quality training dataset. We first framed the deep neural network representation as a nonlinear extension of the linear subspace model, then used it to represent and reconstruct MRE image repetitions from undersampled k-space data. The network weights were learned using a multi-level k-space consistent loss. To further enhance reconstruction quality, phase-contrast specific magnitude and phase priors were incorporated, including the similarity of anatomical structures and smoothness of wave-induced harmonic displacement. Experiments were conducted using both 3D gradient-echo spiral and multi-slice spin-echo spiral MRE datasets. Compared to the conventional linear subspace-based approaches, the nonlinear network representation method was able to produce superior image reconstruction with suppressed noise and artifacts from a single in-plane spiral arm per MRE repetition (e.g., 2mm isotropic resolution in 1 min with a total R=10), yielding comparable stiffness estimation to the fully sampled data. This work demonstrated the feasibility of using deep network representations to model and reconstruct MRE images from highly-undersampled data, a nonlinear extension of the subspace-based approaches.
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.
Three-dimensional multi-echo MRI provides rich anatomical and quantitative information, but repeated volumetric encoding prolongs acquisition and motivates k-space undersampling. Reconstructing undersampled multi-echo data requires exploiting shared anatomy while preserving echo-dependent signal variation; full-volume modeling also introduces substantial computational and memory demands. We propose MIGA, a scan-specific framework comprising shared anisotropic Gaussian geometry, a coordinate-conditioned multi-output amplitude network, and explicit echo-specific phase variables. The Gaussian geometry provides common spatial support across echoes, the implicit network models spatially structured amplitude variations, and the phase variables retain echo-specific complex signal information. All components are jointly optimized using only the acquired multi-coil k-space, requiring no fully sampled training data. Experiments showed that MIGA consistently outperformed the comparison methods across imaging tasks and acceleration factors, with larger improvements under stronger undersampling. MIGA also achieved a favorable quality-cost balance among the evaluated full-volume multi-echo methods. These results support the effectiveness of combining shared Gaussian geometry with implicit echo-dependent amplitude modeling for accelerated 3D multi-echo MRI reconstruction.