Organizations: Medical AI Research Centre, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, Guangdong, China · School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, Guangdong, China · School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, China · Paul C. Lauterbur Research Centre for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, Guangdong, China
Fully unsupervised deep generative modeling (FU-DGM) offers significant potential for compressively sampled magnetic resonance imaging (CS-MRI) reconstruction. Representative FU-DGM formulations, such as deep image prior (DIP) and implicit neural representation (INR), employ architectural bias to induce a low-dimensional manifold in the image space that aligns with the forward observation. However, as the underlying inverse system is highly ill-posed, prolonged iterative fitting in FU-DGM typically leads to poor efficiency and noise amplification. In this paper, guided by the cognitive principle of easy-to-hard learning, we propose CogGen, an FU-DGM framework that reformulates CS-MRI reconstruction as a staged inversion problem. Specifically, CogGen implements an self-paced curriculum learning (SPCL)-driven progressive scheduling strategy through an MRI-aware dual-threshold weighting criterion, which adaptively regulates k-space measurement participation. The data-consistency residual thresholding evaluates the fitting reliability of the current generator, while the k-space radius thresholding controls stage-wise measurement exposure, thereby avoiding uniform fitting throughout optimization. Theoretically, our analysis shows that, when early stages favor easy-to-fit measurements, CogGen yields a reduced local sufficient-iteration bound and a smaller cumulative noise-amplification bound, explaining the improved convergence behavior and reconstruction fidelity of CogGen within a finite iteration budget. Numerical experiments demonstrate that both CogGen instantiations, CogGen-DIP and CogGen-INR, achieve superior performance over prevailing CS-MRI reconstruction techniques, including unsupervised and supervised pipelines.
Figures & tables
Fig. 1: Cognitive-load view of CogGen: measurements with lower load exhibit higher learning utility and are therefore selected earlier, whereas high-load measurements with reduced suitability are deferred to the further stages.
Fig. 2: Reconstruction results on Data #1 at AF = 8. (a)-(j): DIP-TV, BM3D-FISTA, DISCUS, SSDU, aSeq-DIP, Hash-INR- ℓ2 - ℓ1 , PDAC, MoDL, CogGen-DIP and CogGen-INR. The corresponding error maps are presented in the bottom row, alongside the GT and downsampling mask displayed at the far left.
Fig. 3: Reconstruction results on Data #2 at AF = 6. (a)-(j): DIP-TV, BM3D-FISTA, DISCUS, SSDU, aSeq-DIP, Hash-INR- ℓ2 - ℓ1 , PDAC, MoDL, CogGen-DIP and CogGen-INR. The corresponding error maps are presented in the bottom row, alongside the GT and downsampling mask displayed at the far left.
Fig. 4: Evolution of sample selection across five stages ( C1 - C5 ), showing the expansion from central k-space to the full acquired pattern. Top: Data #1 (2D, w=1 ). Bottom: Data #2 (1D, w=0.8 ). Here, C5 denotes the final stage, which contains the original undersampled k-space measurements.
Methods
Data #1 (2D, AF = 8)
Data #2 (1D, AF = 6)
RLNE ROI (%)
PSNR ROI (dB)
RLNE ROI (%)
PSNR ROI (dB)
DIP-TV
9.84
38.17
6.87
30.65
BM3D-FISTA
9.60
38.45
6.28
31.42
DISCUS
8.59
38.91
5.66
32.32
SSDU
8.52
38.91
4.83
33.79
aSeq-DIP
8.41
39.24
5.42
32.77
TABLE I: Quantitative results ( RLNEROI and PSNRROI ) on Data #1 (2D, AF = 8) and Data #2 (1D, AF = 6). The top two performing entries are bolded.
Fig. 5: Performance gains from CogGen on Data #1 (2D, AF = 8) and Data #2 (1D, AF = 6). Integrating CogGen into DIP- and INR-based baselines notably boosts accuracy and convergence under the same iteration budget. (a)-(d): DIP-TV, Hash-INR- ℓ2 - ℓ1 , CogGen-DIP, and CogGen-INR.
Fig. 6: Comparison between MRI-Aware and Random Scheduling on Data #3 at an AF of 5. (a)-(c): DIP-TV, SRS-DIP, CogGen-DIP; (d)-(f): Hash-INR- ℓ2 - ℓ1 , SRS-INR, CogGen-INR. The corresponding error maps are presented in the bottom row, alongside the GT and downsampling mask displayed at the far left.
Methods
Data #3 (1D, AF = 5)
RLNE ROI (%)
PSNR ROI (dB)
DIP-TV
8.13
37.58
SRS-DIP
7.96
37.76
CogGen-DIP
6.04
40.13
Hash-INR- ℓ2 - ℓ1
7.01
38.86
SRS-INR
6.95
38.95
TABLE II: Quantitative evaluation of MRI-aware vs. random scheduling on Data #3 at AF = 5.
Fig. 7: Influence of stage count on Data #4 at AF = 10. Performance peaks at C4 and decreases when additional stages are introduced, highlighting the importance of appropriate stage-count selection for reconstruction performance.
Fig. 8: Single-mode vs. dual-mode thresholding (Data #4 , AF = 10). Dual-mode scheduling enhances detail recovery and reconstruction fidelity. (a-d): Hash-INR- ℓ2 - ℓ1 , CogGen CL -INR, CogGen SPL -INR and CogGen-INR.
Methods
Data #4 (2D, AF = 10)
RLNE ROI (%)
PSNR ROI (dB)
Hash-INR- ℓ2 - ℓ1
8.89
39.10
CogGen CL -INR
8.41
39.59
CogGen SPL -INR
8.29
39.71
CogGen-INR
8.14
39.88
TABLE III: Quantitative comparison for two thresholding schemes on Data #4 (AF = 10).
Accelerated MRI reconstruction recovers diagnostic images from undersampled k-space data to reduce scan time while preserving anatomical and quantitative information.
Generative MRI reconstruction maps an initial source distribution to the target image distribution along a learned recovery trajectory. Common generative methods, such as diffusion and flow, typically learn fine-grained local dynamics whose integration defines this global mapping, hence requiring many network evaluations at inference. Existing few-step sampling approaches can lower computational burden by approximating large transformations from local dynamics, albeit at the expense of reconstruction fidelity. FLEX-MRI instead partitions recovery into a small number of finite intervals between retained states defined by progressive changes in k-space support, and directly learns the reconstruction change across each interval. Because such finite transitions can admit multiple plausible outcomes, FLEX-MRI combines support-relaxed finite-transition learning with stochastic exploration. During training, randomized k-space sampling masks define finite-transition targets with varying support, while the prediction loss remains unrestricted by each individual mask. At inference, FLEX-MRI perturbs a random subset of currently estimated k-space coefficients, allowing the learned predictor to stochastically explore alternative transition paths. Each predicted state is then reconciled with the acquired measurements through data consistency. We theoretically show that this stochastic exploration induces nonzero transition-level variation through the learned recovery map and data consistency without requiring an auxiliary generative sampler. Experiments on multi-coil MRI datasets show that FLEX-MRI outperforms competing methods while maintaining computational efficiency comparable to few-step baselines.
Muhammad Usama Mirza, Esin Öztürk Işık, Tolga Çukur
Dept. of Electrical-Electronics Engineering and National Magnetic Resonance Research Center (UMRAM), Bilkent University, Ankara, Turkey, 06800 · Institute of Biomedical Engineering, Bogazici University, Istanbul, Turkey, 34684
Diffusion models (DMs) have emerged as powerful generative priors for MRI reconstruction with promising results. Yet DM-based methods require extensive iterative refinement, limiting their practical deployment. Consistency models (CMs) provide a compelling alternative, aiming to map out the diffusion trajectory in a single pass, enabling faster generation. In this work, we propose CM-RED, a novel MRI reconstruction method that integrates a pretrained CM into the regularization by denoising (RED) scheme. Our method builds on accelerated proximal gradient RED (RED-APG), and further incorporates controlled noise injection during the update steps to enhance generative diversity and accelerate convergence. Extensive experiments on the fastMRI knee and brain datasets demonstrate that CM-RED achieves high-quality reconstructions across multiple anatomies, contrast weights, acceleration factors, and undersampling patterns, using only 4 network function evaluations (NFEs). The proposed method consistently outperforms existing DM- and CM-based approaches in both quantitative metrics and visual fidelity, and exhibits strong robustness to hyperparameter variations, highlighting CM-RED as an efficient and effective generative framework for accelerated MRI reconstruction. The source code and pretrained models are publicly available at https://github.com/MerveGulle/CM-RED.
Merve Gülle, Junno Yun, Yaşar Utku Alçalar +1
Department of Electrical and Computer Engineering, University of Minnesota, MN, USA · Center for Magnetic Resonance Research, University of Minnesota, MN, USA
Task-adapted compressed sensing magnetic resonance imaging (CS-MRI) is emerging to address the specific demands of downstream clinical tasks with significantly fewer k-space measurements than required by Nyquist sampling. However, existing task-adapted CS-MRI methods suffer from the uncertainty problem for medical diagnosis and cannot achieve adaptive sampling in end-to-end optimization with reconstruction or clinical tasks. To address these limitations, we propose the first task-adapted CS-MRI from the information-theoretic perspective to simultaneously achieve probabilistic inference for uncertainty prediction and adapt to arbitrary sampling ratios and versatile clinical applications. Specifically, we formalize the task-adapted CS-MRI optimization problem by maximizing the mutual information between undersampled k-space measurements and clinical tasks to enable probabilistic inference for addressing the uncertainty problem. We leverage amortized optimization and construct tractable variational bounds for mutual information to jointly optimize sampling, reconstruction, and task-inference models, which enables flexible sampling ratio control using a single end-to-end trained model. Furthermore, the proposed framework addresses two kinds of distinct clinical scenarios within a unified approach, i.e., i) joint task and reconstruction, where reconstruction serves as an auxiliary process to enhance task performance; and ii) task implementation with suppressed reconstruction, applicable for privacy protection. Extensive experiments on large-scale MRI datasets demonstrate that the proposed framework achieves highly competitive performance on standard metrics like Dice compared to deterministic counterpart but provides better distribution matching to the ground-truth posterior distribution as measured by the generalized energy distance (GED).
Xinyu Peng, Ziyang Zheng, Wenrui Dai +5
Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China. · Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China. · Department of Computer Science, City University of Hong Kong, Hong Kong SAR, China. +1