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Physics-informed denoising method for image reconstruction in quantitative low-field MRI

Catarina Redshaw Kranich, Claudia Prieto, Christoph Kolbitsch, Felix Frederik Zimmermann

arXiv:2609.12966v1eess.IV

TL;DR

Low-field quantitative MRI is hampered by low SNR, long acquisitions, and limited access to high-quality training data. This paper proposes an unrolled end-to-end reconstruction method that transfers across field strengths, sequences, and anatomies; on 0.55 T knee T2 mapping, its median absolute difference was below 4 ms.

  • Problem

    Low-field quantitative MRI combines low SNR and long scans with a shortage of high-quality training data for deep-learning reconstruction.

    Source: §1 · pp. 2–3

  • Method

    An unrolled end-to-end network reconstructs quantitative maps directly from k-space using parameter denoising, signal estimation, and data consistency.

    Source: §1 · p. 3, §2.2.4 · p. 7

  • Results

    On the 0.55 T knee test dataset, median absolute difference was below 4 ms; mean absolute difference was 4.31 ± 1.30 ms, versus 4.98 ± 1.53 ms for Mantis, 10.54 ± 2.84 ms for the subspace method, and 11.01 ± 3.07 ms for the direct method.

    Source: §4.2 · p. 14

  • Takeaways & Limitations

    The approach transferred from 0.55 T knee T2 mapping to 0.6 T brain T2 mapping and 72 mT knee T1 mapping without additional acquired training data.

    Source: §5 · p. 19

    Datasets 2 and 3 lacked ground truth, preventing quantitative evaluation; differences from direct reconstruction therefore measured agreement rather than accuracy.

    Source: §5 · p. 20

Abstract

from arXiv · show

Low-field magnetic resonance imaging (MRI) is becoming increasingly important for medical imaging because it can reduce healthcare costs while ensuring high diagnostic output. Nevertheless, quantitative imaging in low-field MRI faces challenges, such as low signal-to-noise ratio and long scan durations. Deep learning approaches have been proposed for image reconstruction to overcome these challenges. Still, deep learning often requires large high-quality training datasets which are usually not available for low-field applications. Here we propose a modular unrolled end-to-end deep learning method for the denoised reconstruction of quantitative parameter maps directly from k-space data for low-field MRI. It consists of three sub-networks that are iteratively applied. They are used for the regularization of the quantitative parameter estimation, as well as for the signal estimation that is based on simulated signal curves. It generalises well and can be applied to different field strengths and even different quantitative MR sequences without the need for new training data. We applied the presented method to noisy data of knees acquired at 0.55 T for the reconstruction of $T_2$-maps and compared it to other classical and deep learning methods. We also applied the proposed approach to $T_1$-mapping of knees at 72 mT and $T_2$-mapping of brains at 0.6 T. The presented approach outperforms the other reconstruction methods with a median difference below 4 ms to the ground truth $T_2$-map. Even though the network was trained with $T_2$-maps acquired at 0.55 T, it successfully denoised data acquired at different field strengths, sequences, and of different anatomies. As a result, the proposed network and its underlying method offer an efficient and flexible solution to denoise low-field MR data and make quantitative low-field MRI a feasible diagnostic tool for clinical applications.

1 Introduction

Low-field quantitative MRI is challenging because low SNR and repeated acquisitions make scans long. Deep-learning reconstruction is constrained by scarce high-quality low-field training data, motivating an approach designed to generalize across domains.

1 Introduction

  • Low-field quantitative MRI faces low signal-to-noise ratio and longer scan times because mapping requires repeated acquisitions with varying parameters.These factors make clinically feasible scan times challenging.Source: §1 · p. 2
  • Deep-learning reconstruction can enforce data consistency, but these networks require high-quality training data that are difficult to obtain for low-field MRI.Using high-field training data can create a generalization gap on low-field data.Source: §1 · p. 3
  • The proposed unrolled end-to-end method reconstructs quantitative maps directly from k-space and is designed to generalize across field strengths, anatomies, and quantitative parameters without domain-specific high-quality retraining.Its parameter and signal-estimation components can be adapted using synthetic signal curves; the method was evaluated on 0.55 T knee T2 mapping and transferred to 0.6 T brain T2 mapping and 72 mT knee T1 mapping.Source: §1 · p. 3

2 Methodology

The methodology reconstructs quantitative maps directly from acquired k-space data and introduces the reconstruction problem before explaining the network components.

2 Methodology

  • The approach reconstructs quantitative maps directly from acquired k-space data.Source: §2 · p. 3
  • The methodology first presents the general qMRI reconstruction problem and then explains the proposed network components.Source: §2 · p. 3
  • The network components are presented as the subsequent focus after the general reconstruction problem.Source: §2 · p. 3

2.1 qMRI Reconstruction Problem

The qMRI reconstruction problem estimates quantitative parameter maps from acquired k-space data. Noise and undersampling make the inverse problem ill-posed, motivating regularization.

2.1 qMRI Reconstruction Problem

  • qMRI uses acquired k-space data to determine maps of one or more quantitative parameters.The parameter vector p contains Np quantitative parameters.Source: §2.1 · p. 4
  • The forward model maps parameter maps through the signal model and encoding operator to k-space data, with random Gaussian noise added.The encoding operator can combine sampling, Fourier transformation, and coil sensitivities.Source: §2.1 · p. 4
  • Noise and potential undersampling make recovery of parameter vectors from acquired k-space commonly ill-posed, so regularization is needed for a robust solution.The regularization term constrains the parameter vectors.Source: §2.1 · p. 4

2.2 Proposed Method

The method unrolls variable splitting into alternating image-data and parameter updates, using learned parameter estimation, denoising, and signal simulation within an iterative data-consistency loop.

2.2 Proposed Method

  • Variable splitting turns reconstruction into alternating image-data and quantitative-parameter updates repeated for J iterations.The image update solves for auxiliary variables, while the parameter update combines parameter estimation and regularization.Source: §2.2 · pp. 4–5

2.2.1 Update of image data

  • The image-data update solves a linear system with conjugate gradients and unrolled differentiation to obtain the next image estimate.The system is written Ax = b, with A and b incorporating the encoding operator, acquired k-space, regularization parameter, and q(pj).Source: §2.2.1 · p. 5

2.2.2 Update of quantitative parameters

  • The parameter update uses Hθ to estimate quantitative parameters, then Pχ to approximate the regularizer’s proximal step and produce pj.The parameter-estimation subproblem is nonlinear, often non-convex, and may have non-unique solutions.Source: §2.2.2 · pp. 5–6

2.2.3 Signal simulation

  • A pre-trained signal sub-network Qϕ acts as a differentiable, faster surrogate for the complex MR signal model and can be exchanged for different signal models and parameters.This exchange supports use with signal models for different quantitative MRI applications.Source: §2.2.3 · p. 6

2.2.4 Network structure

  • Each iteration maps k-space to images, estimates and denoises parameter maps, synthesizes signal images, and applies data consistency; the final Pχ output is the quantitative map.The approach comprises three sub-networks and a data-consistency step, iterated J times.Source: §2.2.4 · pp. 6–7, Figure 1 · p. 7

2.3 Implementation

The implementation uses three specialized sub-networks: pixelwise parameter estimation and signal synthesis, plus spatial parameter-map denoising. Training combines pretrained signal simulation with end-to-end parameter and denoiser learning.

2.3 Implementation

  • The implementation comprises Hθ for parameter estimation, Pχ for denoising, and Qϕ for signal synthesis.Qϕ is the component pretrained before training the proposed approach.Source: §2.3 · p. 7, §2.3.3 · p. 9, §2.3.4 · p. 9

2.3.1 Sub-network Hθ

  • Hθ is a pixelwise multilayer perceptron that maps multi-time-point signal images to quantitative parameters.Its inputs concatenate real and imaginary signal parts, and softplus is used for parameters expected to be positive.Source: §2.3.1 · p. 8

2.3.2 Sub-network Pχ

  • Pχ is a residual U-Net applied separately to parameter maps, with its denoised output added to the noisy input.The network has three encoding and three decoding layers and about 5.7 million trainable parameters.Source: §2.3.2 · p. 8

2.3.3 Sub-network Qϕ

  • Qϕ is a pixelwise MLP that maps quantitative parameters to real and imaginary signal components, scaled by M0 to form complex signals.It is the only component pretrained before the proposed network is trained.Source: §2.3.3 · pp. 8–9, §2.3.4 · p. 9

2.3.4 Training

  • Training fixes pretrained Qϕ, trains Hθ within the larger network and Pχ end-to-end, and supervises intermediate and final parameter estimates against masked ground truth.Hθ is separately trained for Datasets 2 and 3; Pχ does not require retraining for different signal models or parameter sets.Source: §2.3.4 · pp. 9–10

3 Experiments

Experiments trained and evaluated the method on simulated 0.55 T knee data, compared it with classical and deep-learning reconstructions, and tested transfer to other scanners, sequences, and anatomy.

3.1 Training and evaluation data

  • Dataset 1 used simulated k-space from ten subjects’ 0.55 T knee M0- and T2-maps, with added noise and a 70/10/20 train-validation-test split.The dataset contained 2,400 slices; echo times ranged from 16 to 160 ms, and the scans used an 80 × 80 matrix.Source: §3.1 · p. 10

3.2 Application data

  • Application data comprised 72 mT knee T1-mapping with a 3D STIR sequence and 0.6 T brain T2-mapping with a multi-coil T2 GraSE sequence.The knee dataset included five subjects and the brain dataset ten subjects.Source: §3.2 · p. 11

3.3 Training settings

  • Training used four unrolled iterations and optimized the sub-networks’ parameters together with residual and regularization factors.Qϕ pretraining used 100,000 random parameter samples; Hθ was separately trained for Datasets 2 and 3.Source: §3.3 · pp. 11–12

3.4 Comparison to other methods

  • The Dataset 1 comparison included direct reconstruction and PCA-subspace reconstruction with dictionary matching, alongside the deep-learning method Mantis.Methods were assessed visually and by mean absolute difference from masked ground-truth T2 maps across 480 test slices.Source: §3.4 · pp. 12–13

3.5 Generalization Study

  • The generalization study adjusted the signal model and parameters for Dataset 2 T1 mapping and Dataset 3 T2 mapping, retraining Hθ and Qϕ on synthetic signal curves.Dataset 3 retained a mono-exponential decay model with different decay times; Dataset 2 used an inversion-recovery model.Source: §3.5 · p. 13

4 Results

On Dataset 1, the proposed reconstruction produced lower test-set mean absolute differences than direct, subspace, and Mantis methods. It was also applied to T1 knee mapping at 72 mT and T2 brain mapping at 0.6 T.

4.1 Application on evaluation dataset

  • For three exemplary Dataset 1 slices, predicted T2 values match ground truth well, although many pixels differ by up to 10 ms.Figure 2 shows the ground-truth and predicted T2 maps.Source: §4.1 · p. 13, Figure 2 · p. 14

4.2 Comparison to other methods

  • Figure 3 compares the proposed T2 maps with direct, subspace, and Mantis reconstructions, including difference maps to ground truth.The proposed method is reported to produce better maps than classical approaches and the Mantis reference method.Source: §4.2 · pp. 13, 15, Figure 3 · p. 15
  • 4.31 ± 1.30 ms mean absolute difference for the proposed method, versus 11.01 ± 3.07 ms for direct, 10.54 ± 2.84 ms for subspace, and 4.98 ± 1.53 ms for Mantis.Figure 4 presents boxplots of mean absolute differences for all four methods across the 480-slice test dataset.Source: §4.2 · p. 14, Figure 4 · p. 16, §4.3 · p. 16

4.3 Generalization study

5 Discussion

The proposed method outperformed direct reconstruction, the subspace method, and Mantis on Dataset 1, while transferring across field strengths, anatomies, and signal models. Quantitative evaluation of its Dataset 2 and 3 results was limited by missing ground truth.

5 Discussion

  • Dataset 1 mean absolute differences were under 8.6 ms, and the proposed approach outperformed Mantis, the subspace method, and direct reconstruction.The discussion notes remaining differences in the outer bone area, which could potentially improve with more U-Net encoding and decoding layers in denoiser Pχ.Source: §5 · p. 19
  • The method transferred from knee T2 mapping at 0.55 T to brain T2 mapping at 0.6 T and knee T1 mapping at 72 mT, and also handled multi-coil data.Its pixel-wise parameter and signal-estimation subnetworks support anatomy independence; adapting to other signal models requires retraining Hθ and Qϕ on synthetic data, without additional acquired training data.Source: §5 · p. 19
  • Missing ground truth for Datasets 2 and 3 prevented quantitative evaluation; differences from direct reconstruction measure agreement, not accuracy.The difference images were mainly noise-like, without strong anatomical features, which the authors interpret as hinting at successful transfer without induced hallucinations.Source: §5 · p. 20

6 Conclusion

The paper presents a deep learning approach for reconstructing quantitative low-field MR maps directly from k-space. It reports accurate maps across datasets that differ in quantitative parameters, anatomy, and magnetic field strength.

6 Conclusion

  • The approach reconstructs quantitative low-field MR maps directly from acquired k-space data.Source: §6 · p. 20
  • The method handles noisy data successfully while maintaining high accuracy.Source: §6 · p. 20
  • The network is presented as an efficient and flexible solution for quantitative low-field MR reconstruction.Source: §6 · p. 20
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