Ground-truth-free deep learning approach for accelerated quantitative parameter mapping with memory efficient learning

Abstract

Quantitative MRI (qMRI) requires the acquisition of multiple images with parameter changes, resulting in longer measurement times than conventional imaging. Deep learning (DL) for image reconstruction has shown a significant reduction in acquisition time and improved image quality. In qMRI, where the image contrast varies between sequences, preparing large, fully-sampled (FS) datasets is challenging. Recently, methods that do not require FS data such as self-supervised learning (SSL) and zero-shot self-supervised learning (ZSSSL) have been proposed. Another challenge is the large GPU memory requirement for DL-based qMRI image reconstruction, owing to the simultaneous processing of multiple contrast images. In this context, Kellman et al. proposed memory-efficient learning (MEL) to save the GPU memory. This study evaluated SSL and ZSSSL frameworks with MEL to accelerate qMRI. Three experiments were conducted using the following sequences: 2D T2 mapping/MSME (Experiment 1), 3D T1 mapping/VFA-SPGR (Experiment 2), and 3D T2 mapping/DESS (Experiment 3). Each experiment used the undersampled k-space data under acceleration factors of 4, 8, and 12. The reconstructed maps were evaluated using quantitative metrics. In this study, we performed three qMRI reconstruction measurements and compared the performance of the SL- and GT-free learning methods, SSL and ZSSSL. Overall, the performances of SSL and ZSSSL were only slightly inferior to those of SL, even under high AF conditions. The quantitative errors in diagnostically important tissues (WM, GM, and meniscus) were small, demonstrating that SL and ZSSSL performed comparably. Additionally, by incorporating a GPU memory-saving implementation, we demonstrated that the network can operate on a GPU with a small memory (<8GB) with minimal speed reduction. This study demonstrates the effectiveness of memory-efficient GT-free learning methods using MEL to accelerate qMRI.

Fig 1. Workflow of this study.

(a) Dataset preparation procedure in this study. (b) Types of data used for training each network. (c) Performance evaluation of each network during testing.US: Undersampled, FS: Fully sampling, SL: Supervised Learning, ZSSSL: Zero-Shot Self-Supervised Learning, SSL: Self-Supervised Learning, SSIM: structural similarity, NRMSE: Normalized Root Mean Squared Error, GT: ground truth, AF: acceleration factor.

Fig 2. Architecture of the image reconstruction model used in this study.

$D_w$ corresponds to denoising in Equation (12) and DC corresponds to data consistency in Equation (13). The multi-contrast US k-space is the input and the multi-contrast reconstruction k-space is the output. Because MRI images are complex-valued, the input and output of the denoising unit are concatenated in real and imaginary parts in the channel dimension direction. US: Undersampled, CNN: Convolutional neural network.

Fig 3. Training strategy in this study.

The figure illustrates the training, validation, and testing procedures for supervised learning, self-supervised learning, and zero-shot SSL. Ω is the original US k-space. Θ, Λ, Ξ, and Γ are subsets of the k-spaces. US: Undersampled.

Fig 4. Simulation procedures for Experiment 1 and Experiment 2.

The blue box represents the simulation process of multi-contrast data. The yellow box illustrates the procedure for generating the fully sampled (FS) and undersampled (US) k-space data and coil sensitivity maps for training and testing in this study. US: Undersampled, FS: Fully sampled, GT: ground truth.

Fig 5. coil arrangement used to simulate multi-coil signals.

(Left) The red cube represents the field of view (FOV), showing the spatial arrangement of the receiver coils. Different colors indicate the wiring patterns of each coil. (Right) A 2D projection of the coil arrangement. Each coil is modeled as a loop coil with a radius of 100 mm.

Fig 6. Reconstructed images of Experiment 1.

(a) Reconstructed T2 images at AF4 - AF12. The unit of the colorbar is ms.SL: Supervised Learning, SSL: Self-Supervised Learning, ZSSSL: Zero-Shot Self-Supervised Learning.

Fig 7. Quantitative evaluation of Experiment 1.

Quantitative evaluation of the reconstructed T2 maps at AF4 - AF12. The evaluation was performed for both the entire region (blue) and the region with T2 ≤ 120 ms (orange), corresponding to Gray Matter (GM) and White Matter (WM). The numerical values above each bar indicate the mean NRMSE. SL: Supervised Learning, SSL: Self-Supervised Learning, ZSSSL: Zero-Shot Self-Supervised Learning.

Fig 8. Reconstructed images of Experiment 2.

(a) Reconstructed T1 images at AF4 - AF12. The unit of the colorbar is ms. SL: Supervised Learning, SSL: Self-Supervised Learning, ZSSSL: Zero-Shot Self-Supervised Learning.

Fig 9. Quantitative evaluation of Experiment 2.

Quantitative evaluation of the reconstructed T1 maps at AF4 - AF12. The evaluation was performed for both the entire region (blue) and the region with T1 ≤ 1000 ms (orange), corresponding to Gray Matter (GM) and White Matter (WM). The numerical values above each bar indicate the mean NRMSE. SL: Supervised Learning, SSL: Self-Supervised Learning, ZSSSL: Zero-Shot Self-Supervised Learning.

Fig 10. Reconstructed images of Experiment 3.

(a) Reconstructed T2 images at AF4 - AF12. The unit of the colorbar is ms.SL: Supervised Learning, SSL: Self-Supervised Learning, ZSSSL: Zero-Shot Self-Supervised Learning.

Fig 11. Quantitative evaluation of Experiment 3.

Quantitative evaluation of the reconstructed T2 maps at AF4 - AF12. The numerical values above each bar indicate the mean NRMSE. SL: Supervised Learning, SSL: Self-Supervised Learning, ZSSSL: Zero-Shot Self-Supervised Learning.

Fig 12. Memory consumption and training time per minibatch in each network parameter settings.

(a) Maximum memory usage as a function of the number of filters, layers, and iterations. The solid blue line represents results with memory-efficient learning (w/ MEL), while the dashed orange line represents results without memory-efficient learning (w/o MEL). (b) Training time per minibatch.