Low-Field MRI Image Reconstruction Using Physics-Informed Deep Learning

Background:

The application of magnetic resonance imaging (MRI) technology in low-field magnetic resonance imaging has gained increasing attention in recent years. Low-field MRI, due to its low cost and simplified maintenance, is considered to have a broad application prospect in various clinical and research environments. For instance, portable low-field MRI scanners are not only easier to operate but can also be used in emergency units and operating rooms. Furthermore, preliminary evaluations suggest that low-field MRI has potential clinical applications in stroke diagnosis, making this technology more attractive in global medical diagnostics. However, the main challenges of low-field MRI include low signal-to-noise ratio (SNR) and strong B0 field inhomogeneity caused by magnet design, material defects, and manufacturing tolerances.

This study, completed by scholars David Schote, Lukas Winter, Christoph Kolbitsch, Georg Rose, Oliver Speck, and Andreas Kofler, was published in IEEE Transactions on Biomedical Engineering in 2023. The research aims to address the distortion and noise issues in low-field MRI images by combining physics knowledge with deep learning, thereby improving image quality and diagnostic accuracy.

Methodology:

This research proposes a model-driven image reconstruction method based on an unfolded neural network, called SH-Net (Spherical Harmonic Network), which ensures the smoothness of spatial field map estimation by estimating spherical harmonic coefficients. This network, through an end-to-end trainable model, jointly estimates the B0 field map and image reconstruction. The experiment used low-field data of the human knee for retrospective simulation, comparing the performance of the model with other model-driven methods under different noise levels and various B0 field distributions.

Specific process includes:

1. Data Acquisition and Preprocessing:
   This study used three-dimensional single-coil spin-echo knee data from the FastMRI dataset. Each sample selected a two-dimensional slice, resulting in a total of 973 different complex-valued samples. During the training, validation, and testing stages, 1260 (70%), 360 (20%), and 180 (10%) images were generated respectively.

2. SH-Net Architecture Design:
   SH-Net estimates the spherical harmonic coefficients of the complex-valued input images through an encoding path, setting a fixed number of 16 feature channels, and maps the coefficients to spherical harmonic coefficients through fully connected layers. The network aims to generate coefficients within the 5th order, which is sufficient to describe the field map.

3. Regularization Term Neural Network:
   The study adopts two different neural network architectures for field map estimation and image denoising. For denoising, a residual connection U-shaped network (U-Net) is used. Assuming a good field map estimation has already been obtained, the U-Net is applied for image denoising based on the B0 field map corrected for geometric distortions.

4. Optimization Strategy:
   The improved algorithm consists of two alternating sub-problems that optimize the field map and the image respectively. To enhance training efficiency, a pre-training strategy for neural networks is employed, pre-training SH-Net and U-Net separately for their relevant tasks, followed by end-to-end training.

5. Experimental Design:
   Experiments with different alternating times were conducted to study the impact of alternating optimization on reconstruction results. The pre-trained neural networks used the Adam optimizer, and regularization coefficients were optimized during training. Finally, the optimal alternating time of t=3 was determined for subsequent results analysis.

Results:

1. Field Map Estimation Results:
   SH-Net consistently showed a lower mean absolute error (MAE) across different noise levels, significantly outperforming phase difference maps and the existing residual convolutional neural network (ORN) method. The MAE across the entire field map was 324.7±145.3Hz (σ_y=0.2), with even lower errors within the regions of interest (ROI).

2. Image Reconstruction Results:
   The unfolded optimization algorithm trained end-to-end was compared against FFT reconstruction without B0 knowledge, joint modeling, and dual modeling methods under different noise levels:

   • RMSE (Root Mean Squared Error):
     At σ_y=0.2, the RMSE of the SH-Net training method was 0.1386, significantly lower than joint and dual modeling methods.
   • PSNR (Peak Signal-to-Noise Ratio):
     At σ_y=0.2, the PSNR of the SH-Net method was 28.058, higher than other methods.
   • SSIM (Structural Similarity Index):
     At σ_y=0.2, the SSIM of the SH-Net method was 0.6906, much higher than other methods.

3. Comprehensive Comparison:
   Combining quantitative indicators and the visual quality of the reconstructed images, the SH-Net method excels in correcting geometric distortions and improving image SNR, demonstrating better stability and robustness, especially under higher noise levels.

Conclusion and Significance:

This study proposes a novel image reconstruction method for low-field MRI. By combining physical knowledge with deep learning, it achieved significant results in jointly correcting B0 inhomogeneity and improving image SNR. The method is not only applicable to single scans, reducing acquisition time but also holds substantial potential for actual clinical applications. Future work can further extend to non-Cartesian trajectories and actual low-field MRI data.

Highlights:

• Innovatively proposed the SH-Net architecture, ensuring spatial smoothness of field map estimation through a physics-driven deep learning approach.
• Efficient joint optimization strategy significantly enhances the robustness and accuracy of field map and image reconstruction.
• Outstanding performance of the SH-Net method across different noise levels and complex field maps, proving its wide applicability in low-field MRI applications.