Organizations: Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA · Center for Magnetic Resonance Research, University of Minnesota, Minneapolis, MN, USA · Department of Medicine (Cardiology), University of Minnesota, Minneapolis, MN, USA
MRI reconstruction methods for undersampled k-space data naturally utilize complex-valued measurements. Parallel developments in sparse phase retrieval have shown that magnitude-only measurements may provide complementary information for signal recovery. However, their use in MRI reconstruction remains largely unexplored, due to lack of practical settings where informative magnitude measurements can be obtained without additional scan time. In this work, we investigate the use of auxiliary k-space magnitude information for accelerated steady-state dynamic MRI reconstruction, and demonstrate strong consistency of k-space magnitudes across time-frames. Building on this observation, we propose C+Mag, a magnitude-informed physics-driven deep learning reconstruction method. The proposed method employs an ADMM-based unrolling framework with a novel magnitude-aware data-fidelity formulation, where quadratically smoothed optimization and momentum-based updates are introduced to address the non-differentiability and non-convexity of the magnitude constraints. Experiments on retrospectively undersampled cine MRI and phase-contrast flow MRI datasets, as well as prospectively undersampled real-time cine MRI acquisitions, demonstrate improved artifact suppression, sharper anatomical recovery, and better preservation of phase information compared to conventional PD-DL methods, which is further supported through blinded expert reader evaluations.
Figures & tables
Fig. 1: Cosine similarity between the central cardiac phase and all other phases, computed from fully sampled magnitude k-spaces across five slices from five different subjects. Different colors correspond to different subjects, while the shaded regions denote the standard deviation across slices. The strong similarity suggest that k-space magnitude information from neighboring cardiac phases can be used as auxiliary information without increasing scan time.
Fig. 2: C+Mag reconstruction pipeline that integrates both complex-valued and magnitude-only measurements. Acceleration rate R=3 is used for illustration, without loss of generality. For the cardiac phase of interest t , the complex-valued measurements, yΩt , are used for reconstruction, both in regular PD-DL and in proposed C+Mag . From adjacent cardiac phases t+1 and t+2 , only the magnitude of the k-space data on lines specified by Ωt+1 and Ωt+2 are used as auxiliary information in C+Mag , denoted by rΔ with Δ=Ωt+1∪Ωt+2=ΩtC, and C denotes the complement set. Note rΔ is readily available without any changes to the cine MRI acquisition. Learnable parameters corresponding to each unroll are highlighted using subscripts.
Fig. 3: Representative reconstructions from cine MRI data with R={6,8} , acquired on 0.55T, 1.5T, and 3.0T scanners. Conventional PD-DL methods introduce artifacts and fail to preserve anatomical structures (yellow arrows), while also exhibiting noticeable blurring. In contrast, our proposed method effectively mitigates these artifacts and preserves image sharpness.
Fig. 4: Representative reconstruction results for phase-contrast flow MRI at acceleration factors R∈{6,8} . The first row for each acceleration factor shows the reconstructed magnitude images, followed by the corresponding error maps ( ×10 ) and phase difference maps ( Δϕ ). Conventional PD-DL methods exhibit residual artifacts and phase inconsistencies (yellow arrows), whereas the proposed method substantially suppresses these artifacts and preserves both magnitude and phase information.
Fig. 5: Reconstruction examples from prospectively undersampled bSSFP (top) and GRE (bottom) real-time cine data at R=8 . tGRAPPA at the clinical acquisition ( R=4 ) is used as the baseline for the bSSFP dataset. For the GRE dataset, the data were prospectively acquired at R=8 and there is no R=4 baseline. Standard tGRAPPA reconstruction and conventional PD-DL methods at R=8 exhibit residual artifacts and loss of anatomical detail (yellow arrows), both in systolic and diastolic phases. The proposed C+Mag method preserves cardiac structures and suppresses reconstruction artifacts.
Fig. 6: Results of the blinded expert reader evaluation for segmented cine and phase-contrast flow acquisitions at R=6 and R=8 . Bar plots show the mean reader scores and standard deviations for perceived SNR, blurring, aliasing artifacts, and overall image quality, where lower scores indicate better image quality. Statistical significance was assessed using Wilcoxon signed rank test. Across both datasets, the proposed C+Mag reconstruction achieved scores comparable to the reference standard, while consistently outperforming conventional PD-DL reconstructions.
ProxR(⋅)
DF Solver
Smoothing
Unrolling
PSNR
SSIM
TE-UNet ( ♠ )
GD
Quad-S
ADMM
35.60
0.936
TE-UNet ( ♣ )
GD
Quad-S
ADMM
36.13
0.947
ResNet ( ♠ )
GD
Quad-S
ADMM
35.82
0.933
ResNet ( ♣ )
GD
Quad-S
ADMM
35.83
0.935
TE-UNet ( ♣ )
GD
Quad-S
ADMM
36.13
0.947
TE-UNet ( ♣ )
Adam
Quad-S
ADMM
32.79
0.868
TABLE IV: Ablation study on the reconstruction architecture, DF solver, smoothing operator, and unrolling strategy. The best-performing configuration in each panel is highlighted , overall best result is shown in bold . ( ♠ ) and ( ♣ ) denote shared and unshared DF parameters ( λ,μ,β ), respectively.
MRI reconstruction from undersampled k-space measurements is an ill-posed inverse problem. Physics-driven deep learning (PD-DL) methods have shown strong performance for this task by combining the MRI forward model with learned image regularization within algorithm-unrolling frameworks. However, most existing PD-DL methods reconstruct complex-valued images directly, thereby implicitly coupling magnitude and phase within a single learned representation. This coupled regularization may be suboptimal in reconstruction settings where accurate phase modeling plays an important role, such as partial Fourier (PF) imaging, where recovery of the omitted asymmetric k-space measurements depends on the underlying image phase. In such scenarios, explicit modeling of magnitude and phase as separate components may reduce the reliance on externally estimated or predefined phase information. To this end, we propose UMPIRE-Net (Unrolled Magnitude-Phase In REgularization Network), a PD-DL method that introduces separate learned regularizers for magnitude and phase components, together with a novel data-fidelity formulation that enforces measurements consistency. We evaluate UMPIRE-Net for accelerated MRI with PF across different datasets and acceleration factors. Experimental results demonstrate that our proposed method improves reconstruction quality compared with a conventional complex-valued PD-DL baseline, yielding sharper images and reduced artifacts. Code available at: https://github.com/MahdiSaberii/UMPIRE-Net
Mahdi Saberi, Toygan Kiliç, Mehmet Akçakaya
Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, USA · Center for Magnetic Resonance Research, University of Minnesota, Minneapolis, MN, USA
Accelerated magnetic resonance imaging (MRI) enabled by the training of deep learning (DL)-based image recon. models requires large and diverse raw k-space datasets. In most clinical MRI applications, due to storage and patient privacy concerns, raw k-space data is discarded and magnitude-only images are the only component saved. Consequently, a large portion of the DL-based MRI recon. literature has either relied on small training datasets or has used one of the few available open-source k-space datasets. At the same time, the growing number of anonymized magnitude-only image registries/databases motivates the development of techniques that can use them as training datasets for generalizable DL-based recon. models. Here we propose to address this challenge by employing a generative approach based on conditional score-based diffusion models (SBDMs): given a magnitude-only MR image, it synthesizes a phase map (in the image domain) that realistically corresponds to the magnitude-only image. We evaluate its generative capabilities in a downstream DL-based recon. task whereby a large k-space dataset is generated by combining the SBDM-synthesized phase-maps and the corresponding magnitude-only images, and this k-space dataset is then used to train a DL model for accelerated MRI recon. We compare the performance of the resulting DL model versus those trained according to (a) a naive approach that uses smooth phase, (b) a k-space training dataset generated using synthesized phase maps derived from a generative adversarial network, and (c) the ground truth k-space data. Our results suggest that the DL model trained from SBDM-synthesized k-space data outperforms the other approaches in terms of quantitative metrics as well as qualitatively observed recon. fidelity, i.e., whether the reconstructed images include erroneous or hallucinated features that could adversely impact diagnostic accuracy.
M. Berk Sahin, Dilek Yalcinkaya, Abolfazl Hashemi +1
Conventional MRI reconstruction methods treat images and coil sensitivities as discrete objects, leading to high memory demands and limited structural awareness that hamper effective regularization. These limitations hinder accurate reconstruction in highly undersampled scenarios, such as dynamic 3D cardiac magnetic resonance (CMR). We introduce a discretization-free, memory-efficient, model-based framework for dynamic 2D and 3D MRI reconstruction from highly undersampled data. We represent magnetization and coil sensitivities as continuous objects -- differentiable functions -- using tensor products of univariate neural fields. This tensor product structure enables scalable optimization in high-dimensional spatiotemporal settings. Our method outperforms state-of-the-art model-based reconstructions in dynamic 2D and 3D MR settings, preserving structure and motion even under aggressive undersampling (e.g., acceleration factor 16).
Ray Sheombarsing, Max van Riel, David Heesterbeek +2
Computational Imaging Group for MRI Therapy & Diagnostics, Department of Radiotherapy, University Medical Center Utrecht, Utrecht, The Netherlands