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Consistency Models for Fast MRI Reconstruction Using Regularization by Denoising
Merve Gülle, Junno Yun, Yaşar Utku Alçalar, Mehmet Akçakaya
TL;DR
Diffusion models provide strong generative priors for MRI reconstruction but require extensive iterative refinement, motivating faster alternatives that retain robustness across acquisition conditions. CM-RED embeds a pretrained consistency model in a RED-APG reconstruction scheme with controlled noise injection, achieving strong reconstruction quality across knee and brain MRI settings with four NFEs and outperforming existing DM- and CM-based solvers.
Problem
Diffusion-based MRI reconstruction can handle acquisition and distribution variations, but typically requires hundreds of NFEs, limiting its applicability in large-scale imaging.
Method
CM-RED uses a pretrained consistency model as a surrogate denoiser within RED-APG, combining prior updates, explicit data fidelity, momentum acceleration, and controlled noise injection.
Results
CM-RED achieves consistently strong quality across knee and brain MRI experiments with only four NFEs, outperforming existing DM- and CM-based solvers in nearly all settings.
Takeaways & Limitations
CM-RED provides a practical, computationally efficient, and reliable generative-model-based strategy for accelerated MRI reconstruction.
Takeaways & Limitations
Existing unrolled and plug-and-play methods can have reduced robustness outside their trained configurations, while denoisers may be mismatched to structured iterative errors rather than Gaussian noise.
Abstract
from arXiv · showhide
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.
1 Introduction
Accelerated MRI reconstruction remains challenging because high acceleration makes it difficult to preserve fidelity while suppressing artifacts, while diffusion-based methods are computationally expensive. CM-RED integrates a pretrained consistency model into RED-APG with controlled noise injection, targeting fast, robust reconstruction across varied MRI settings.
- High acceleration makes MRI reconstruction ill-posed, challenging conventional methods to preserve image fidelity while suppressing artifacts.
- Diffusion-based MRI reconstruction is robust to acquisition and distribution variations but typically requires hundreds of sequential sampling steps.This computational overhead limits use in time-sensitive workflows and large-scale deployment scenarios.
- CM-RED integrates a pretrained consistency model as a learned proximal prior within the RED formulation.The framework is designed to reconstruct accelerated MRI measurements using only a few iterations.
- Controlled noise injection and iteration-adaptive denoising refine RED-APG for consistency models, accelerating convergence and improving robustness across noise conditions.The design also utilizes the generative capabilities of consistency models during reconstruction.
- CM-RED uses unified hyperparameters across anatomies, contrasts, and sampling patterns, with settings differing only by acceleration rate.Moderate parameter perturbations produce robust behavior in the reported experiments.
- CM-RED consistently outperforms existing diffusion- and consistency-model inverse problem solvers while providing a 25×–250× speed-up.The evaluations cover fastMRI knee and brain datasets, with consistency models also trained from scratch for various anatomies.
2 Background and Related Works
MRI reconstruction is an ill-posed inverse problem where learned and generative priors improve flexibility and fidelity but differ in robustness and computational cost. Diffusion models provide strong priors, while consistency models aim to recover clean samples in a single step and reduce sampling burden.
- 2.1 MRI Reconstruction Inverse Problem: MRI reconstruction combines acquired k-space measurements with an encoding operator and a regularizer to recover an image from an ill-posed inverse problem.The regularizer complements data fidelity in the reconstruction objective.
- 2.1 MRI Reconstruction Inverse Problem: Unrolled networks learn data-fidelity and regularization modules for fixed unrolls but often generalize poorly across sampling patterns, acceleration factors, or SNR.Their high reconstruction quality is primarily reported for in-distribution data.
- 2.1 MRI Reconstruction Inverse Problem: PnP methods replace explicit regularizers with pretrained denoisers, but Gaussian-noise training mismatches the complex, non-Gaussian errors in iterative MRI updates.This mismatch may degrade reconstruction quality.
- 2.2 Diffusion Models: Diffusion models combine learned generative priors with physics-based data-fidelity terms, but DPS typically requires hundreds of NFEs and DDS reduces this to approximately 100.DDS remains computationally burdensome despite using conjugate-gradient corrections on a local tangent subspace.
- 2.3 Consistency Models: Consistency models map noisy samples at any diffusion timestep directly to clean estimates, unlike diffusion models’ sequential denoising along the full trajectory.Distilled CMs learn this mapping through consistency across noisy versions of the same clean sample.
- 2.3 Consistency Models: Existing CM-based inverse-problem methods were developed mainly for natural-image restoration, leaving their applicability to MRI reconstruction limited.The cited MRI setting can suffer from residual aliasing artifacts and noise amplification.
3 Methods
CM-RED integrates a pretrained consistency model into RED-APG, combining CM prior updates, data-fidelity enforcement, momentum acceleration, and controlled noise injection. Its four-step process progressively increases CM-driven refinement while solving data fidelity efficiently with conjugate gradients.
- Proposed Method: CM-RED: CM-RED uses a pretrained consistency model as the surrogate denoising operator within RED-APG.The framework combines CM-based prior updates with explicit data fidelity enforcement and momentum acceleration.
- Proposed Method: CM-RED: A weighted interpolation combines the CM output with the previous estimate, increasing CM influence throughout reconstruction.The interpolation enables stronger CM-driven refinement in later iterations.
- Proposed Method: CM-RED: Gaussian noise is injected before CM denoising at every iteration to avoid minor corrective updates at very low noise levels.The paper states that CMs increasingly behave like identity mappings as denoising noise approaches zero.
- Proposed Method: CM-RED: Data fidelity is enforced after the CM update by solving a quadratic penalized least-squares problem with conjugate gradients.The update maintains consistency with measured data while retaining CM-provided generative regularization.
- Proposed Method: CM-RED: Momentum acceleration inherited from RED-APG is applied after the data-fidelity update using a momentum coefficient.Its effects on reconstruction quality and convergence are evaluated empirically.
4 Experimental Setup
CM-RED is evaluated on fastMRI knee and brain MRI under multiple sampling conditions, using a four-iteration reconstruction scheme with scheduled noise, denoising, weighting, penalty, and momentum parameters. Comparisons cover equidistant and Gaussian undersampling at acceleration factors R = 4 and R = 8.
- Datasets: Experiments use complex-valued multi-coil fastMRI knee and brain measurements spanning multiple anatomies and contrast weightings.The datasets include coronal PD and PD-FS knee scans and axial T1-, T2-, and FLAIR-weighted brain scans.
- Implementation: CM-RED uses N = 4 outer iterations, with each data fidelity update solved using 10 conjugate-gradient iterations.The reconstruction parameters control injected noise, CM denoising, CM-output weighting, quadratic penalty, and momentum.
- Noise schedule: The injected noise decreases across iterations from an initial diffusion-index-dependent level controlled by iN and a decay parameter γ > 0.The initial diffusion index determines the first perturbation level, while γ controls how quickly perturbations decay.
- CM denoising: The CM denoising level is allowed to exceed the injected perturbation level through ˜σn = (1 + δn)σn.The iteration-dependent offset δn controls the effective denoising strength.
- Update parameters: CM-output weights increase smoothly toward 1, while the constant quadratic penalty couples the reconstruction estimate to the CM-refined output and momentum is gradually dampened.These schedules transition from data-fidelity-dominated updates toward CM-driven refinement while limiting late-stage oscillation.
- Evaluation protocol: Evaluation uses equidistant and Gaussian masks at R ∈ {4, 8}, with 24 central k-space lines retained except 12 lines for Gaussian R = 8.Baselines include DPS, DDS, and CM4IR, implemented with 1000, 100, and publicly specified CM-based inference evaluations, respectively.
5 Experiments and Results
CM-RED produces strong qualitative and quantitative reconstructions across equidistant and Gaussian undersampling while using only 4 NFEs. Its noise-injection and momentum components jointly improve reconstruction quality and performance across NFE settings, and the method remains robust to moderate hyperparameter perturbations.
- Reconstruction results: CM-RED more consistently suppresses residual artifacts while preserving anatomical detail than DPS, DDS, and CM4IR across evaluated settings.In axial T1-pre reconstructions, the lateral ventricles are more clearly delineated with CM-RED.
- Quantitative comparison: CM-RED achieves the highest PSNR and SSIM in nearly all configurations despite using only 4 NFEs.The exceptions are PSNR for coronal PD-FS at R = 4 with equidistant sampling and R = 8 with Gaussian sampling, where it ranks second-best.
- Robustness: Under independent ±10% hyperparameter perturbations, per-slice PSNR and SSIM differences remain centered near zero for R = 8 Gaussian undersampling.The analysis compares perturbed reconstructions with the nominal configuration.
- Ablation studies: The variant combining controlled noise injection and momentum consistently achieves the highest performance among the four ablation variants.Both components individually improve reconstruction quality, while their combination provides complementary benefits across anatomies and contrasts.
- Ablation studies: With 6 NFEs, the combined noise-injection and momentum configuration reaches performance comparable to the other variants at their convergence point.Across 4–30 NFEs, this configuration consistently achieves the highest PSNR and SSIM.
6 Discussion
CM-RED combines a pretrained consistency-model prior with explicit multi-coil MRI data fidelity, noise injection, and momentum to enable efficient reconstruction. It remains robust across settings, while training and broader acquisition or data-domain coverage remain practical boundaries.
- Method: CM-RED directly uses a consistency-model clean-image estimate within an explicit data-fidelity step, avoiding repeated traversal of a long diffusion trajectory.This enables few-step reconstruction compared with diffusion-model priors.
- Method: Controlled noise injection and momentum jointly improve iterative updates under a limited NFE budget, with their combination performing strongest in ablations.Each component improves reconstruction quality individually, while their combination provides the strongest performance across evaluated settings.
- Robustness: The same hyperparameter configuration was used across anatomies, contrast weightings, and undersampling patterns, with separate settings only for acceleration factors.Moderate parameter perturbations caused limited changes in PSNR and SSIM.
- Method: CM-RED combines a CM prior with quadratic penalized data fidelity based on the multi-coil MRI forward model, addressing limitations of back-projection updates for noisy measurements.The design explicitly enforces consistency with acquired k-space measurements and improves reconstruction quality across fastMRI knee and brain datasets.
- Positioning: CM-RED is intended as an efficient and flexible generative prior for MRI inverse problems rather than a replacement for protocol-matched PD-DL reconstruction networks.Its positioning reflects test-time use of a pretrained prior with the measurement model, without end-to-end retraining for each undersampling pattern.
- Limitations and future work: Training DM and CM priors remains computationally demanding, while broader datasets, non-Cartesian scans, patient cohorts, and measurement-only training are future directions.The current priors were trained using fully sampled datasets, which are not always available in clinical MRI.
7 Conclusion
CM-RED uses pretrained consistency models as learned proximal operators for few-step accelerated MRI reconstruction. Across knee and brain experiments, it achieved strong quality with four NFEs and outperformed existing diffusion- and consistency-model solvers in nearly all settings.
- CM-RED uses pretrained consistency models as learned proximal operators in a few-step MRI reconstruction framework.
- 4 NFEs supported consistently strong reconstruction quality across knee and brain MRI experiments.
- CM-RED outperformed existing DM- and CM-based solvers in nearly all evaluated settings.