Introduction

Low-field MRI (<0.1T) has the potential to expand healthcare access, particularly in low- and middle-income regions^1,2. However, its inherently low signal-to-noise ratio (SNR) presents a challenge in terms of scan time and spatial resolution, affecting detailed pathology detection and diagnosis. Recently, deep learning-based denoising methods have received increasing attention, and have been applied to low-field MRI data sets^3,4. However, supervised learning-based denoising suffers from the lack of high-quality low-field training data, while transfer learning from networks trained on high-field MRI data⁵ requires careful tuning to account for differences in contrast and noise distribution. In this work, we adapted the zero-shot noise2noise (ZS-N2N)⁶ concept for low-field MRI and added an additional “relaxation/contrast” dimension (T₁,T₂) for a self-supervised, fast 4D-denoising in about 10-20 seconds per subject, potentially allowing fewer TI/TE points required for T₁/T₂ fitting.

Methods

Noise2noise⁷ has demonstrated that networks trained on noisy image pairs can achieve similar quality as conventional supervised learning. In ZS-N2N, a single source image can be down-sampled into two sub-images, whose noise shares the same distribution while remaining statistically independent. In this study, given a quantitative MR-parameter mapping dataset (source images) with dimensions (nt,nx,ny,nz), two low-resolution down-sampled images (nt,nx/2,ny/2,nz/2) can be formed by applying two 3D convolutions on the source images, with stride of two and “symmetric” kernels: $$$k_1=\left[\left[\begin{array}{cc}0.25&0\\0&0.25\end{array}\right],\left[\begin{array}{cc}0&0.25\\0.25&0\end{array}\right]\right]$$$ and $$$k_2=\left[\left[\begin{array}{cc}0&0.25\\0.25&0\end{array}\right],\left[\begin{array}{cc}0.25&0\\0&0.25\end{array}\right]\right]$$$, as $$$d_1(y)=y\circledast{k_1}$$$ and $$$d_2(y)=y\circledast{k_2}$$$. In the loss calculation for a given network $$$\hat{x}=f_{\hat{\theta}}(y)$$$, the network parameters are fitted initially with a symmetric residual-learning loss calculated as:$$L_1=\frac{1}{2}\left(\left\|d_1(y)-f_\theta\left(d_1(y)\right)-d_2(y)\right\|_2^2+\left\|d_2(y)-f_\theta\left(d_2(y)\right)-d_1(y)\right\|_2^2\right).$$Here the network is optimized between two down-sampled images $$$d_1(y)$$$,$$$d_2(y)$$$from the same source image. Secondly, the data-consistency loss is calculated by first denoising the source image and then applying down sampling:$$L_2=\frac{1}{2}\left(\left\|d_1(y)-f_\theta\left(d_1(y)\right)-d_1\left(y-f_\theta(y)\right)\right\|_2^2+\left\|d_2(y)-f_\theta\left(d_2(y)\right)-d_2\left(y-f_\theta(y)\right)\right\|_2^2\right).$$This constrains the network output to be consistent with the source image thereby avoiding overfitting to the down-sampled images. The total loss for the optimization would be $$$L_{\text{total }}=L_1+L_2$$$.

To enable a short processing time and avoid overfitting, a simplistic 3D convolutional neural network $$$f_\theta$$$ is used. It incorporates a 3D convolutional neural network structure with three convolutional layers, employing a LeakyReLU activation with a negative slope of 0.2, performing convolutions with kernel sizes of 3x3x3 in the first two layers and 1x1x1 in the third layer. The denoising pipeline is illustrated in Fig.1. For a standard inversion-recovery T₁ mapping dataset with 6 TIs and a matrix size of (6,32,94,70), the network with its modest 70k parameters completes denoising of the entire dataset in less than 20 seconds on an NVIDIA RTX6000 GPU over 2000 epochs.

Four volunteer datasets were acquired on a 46 mT Halbach low-field system¹ for testing using a 3D TSE sequence. Two datasets⁸ were acquired to estimate T₂ of lipid and muscle in the calf muscle with 10 TEs and an echo-spacing of 11 ms, resolution 2.5x2.5x5mm³. Two T₁ mapping⁸ datasets were acquired in brain (2.5x2.5x5mm³), with slightly differing parameters to achieve different contrasts: 1) TR=1250ms and 6 inversion times (TIs): 50,100,150,200,300,500 ms; 2) TR=1200ms and 6 TIs: 50,91,166,302,549,900 ms. The proposed method (4D-dataset, 3D-CNN) was compared to the original ZS-N2N (2D-CNN), two extended 3D versions either by adding the inversion time dimension (version 1) or the z-direction (version 2), and BM4D⁹. A simulated phantom T₁ mapping (50,91,166,302,549,900 ms) study was added to test the performance of the algorithm with 3 noise levels (low,middle,high). To enable zero-mean Gaussian noise distribution of each image, a simple phase correction was performed before denoising to rotate the magnetization to the real-axis¹⁰.

Results

Figure 2 compares different denoising methods, highlighting the finer structures captured with the proposed 4D-denosing approach. Figure 3 evaluates the proposed method over three noise levels using various metrics in simulation, demonstrating increased PSNR/SSIM and reduced nRMSE with respect to the noise-free ground-truth images after denoising. Figure 4 shows T₁ mapping results, contrasting the effects of using different numbers of TIs and the impacts of denoising. Figure 5 shows T₂ mapping, highlighting the consistency and efficiency of our method to reduce scan time.

Discussion and conclusion

In this work, we have proposed a zero-shot denoising approach for low-field quantitative MRI, without training on any other sources. It has demonstrated its potential to allow for less fitting points in T₁,T₂ mapping. This is essential since, e.g., it took roughly 36 minutes⁸ to acquire these 6 TIs datasets, where denoising can really improve the scan-efficiency to reach the same SNR of T₁,T₂ mapping with reduced number of fitting points. However, the optimized choice of TIs/TEs has not been investigated yet, remaining a topic for the future. To further explore the denoising performance of a multi-contrast protocol (e.g. T₁w,T₂w,Flair/DWI) at low-field may also be interesting.

Acknowledgements

No acknowledgement found.