Introduction

The theory of compressed sensing ¹ allowed time reduction in MRI image acquisition by several folds but increased time for image reconstruction. Deep learning (DL) has recently been introduced ^2,3 to allow for fast reconstruction with comparable or improved image quality compared to traditional iterative reconstructions. However, these DL reconstructions are mainly concentrated on Cartesian k-space trajectories. Recent deep learning-based non-cartesian MRI data reconstruction methods are based on simulated non-cartesian resampling from an original Cartesian grid in k-space ^4,5. The simulated non-cartesian sampling may not mimic the non-cartesian MRI data from the real MRI scanning because it does not take into account the noise distribution, gradient inaccuracies, or B0-field inhomogeneities. Here, we evaluated the performance of two deep learning networks on reconstructing the image acquired with one spiral trajectory in k-space, which is an under-sampled k-space (using half of the acquisition time) because 2-interleave spiral trajectories in k-space satisfy the Nyquist sampling rate.

Method

The 3D dynamic Arterial Spin Labeling (dASL) images were acquired on a 3 Tesla GE MR750 scanner using 32-channel receive-only phased array coil at 50 time points from 21 healthy subjects for a different project ⁶. At each time point, ASL images were acquired with two spiral interleaves (uniform density spirals, 2048 points on each spiral, bandwidth of 125 kHz), which were reconstructed using non-uniform FFT (NUFFT) ⁷ to serve as ground-truth images. ASL images were also reconstructed separately from the first (1^st single-spiral image) and second spiral interleave (2^nd single-spiral image) using NUFFT to serve as under-sampled images.

We built a U-shaped convolutional neural network (CNN) (U-Net, Fig. 1) with skip connections between the encoding and decoding layers to learn the process of generating two-spiral target images from one-spiral input images. The images from the first spiral trajectory and those from two spiral trajectories were used in the training as the input and target of the U-Net. Furthermore, a conditional generative network (cGAN) was used to enhance the learning. The same U-Net as in Fig. 1 was used as the generator (Fig. 2, Left) and one more CNN was used as the discriminator with binary output to distinguish the fake and real input pairs (Fig. 2, Right). The input and target images for the generator were the same as those used in the U-Net. The input images for the discriminator are the ground-truth and output images from the generator. Three different loss functions (L1-loss, L2-loss, and SSIM-loss) were used in the U-Net separately, while SSIM-loss was used in the cGAN. Five-fold cross validation (17 subjects for training and 4 subjects for testing at each time) was used to evaluate the performance of the reconstructed images. The images from 2^nd single-spirals were used in the testing only. The performance of each deep-learning method was evaluated by calculating a peak signal-to-noise ratio (PSNR), mean squared error (MSE) and Structural Similarity Index (SSIM) of reconstructed test images by comparing with their corresponding ground-truth images.

Results & Discussion

For U-Net, the learned images from 1st single-spiral test image (Fig. 3a) with the ground-truth two-spiral image (Fig. 3b), are shown from different loss functions: L1-loss (Fig. 3c), L2-loss (Fig. 3d) and SSIM-loss (Fig. 3e). The results demonstrate that the U-Net can reconstruct high-resolution images from half-time under-sampled low-resolution images successfully, and the background noises in the ground-truth image are minimized in the process. The learned images from a 2nd spiral test image are shown in the second row of Fig. 3(f-j). The U-Net, which was trained on 1st single-spiral images, can reach similar performance on the unseen 2nd single-spiral images. The PSNR, MSE and SSIM calculated from learned high-resolution images from 1st single-spiral test images and 2nd single-spiral test images are shown in the Table 1. For the comparison, the PSNR, MSE and SSIM of the low-resolution single-spiral test images are also shown in Table 1. The metrics indicate that the U-Net with SSIM-loss performs slightly better than the L1-loss and L2-loss[MOU1] but does not reach statistical significance. The learned images from cGAN is shown in Fig. 5. cGAN can improve the image quality of the low-resolution image but it also preserves both brain and background noises. [MOU1]Here, we need some figure to support the superior performance of SSIM loss by an image (e.g., the local SSIM map as we discussed) because I cannot see clear difference from the images that you have showed.

Conclusion

Deep-learning models, both U-Net and cGAN are promising in reconstructing high-resolution images from under-sampled spiral images. This study serves as a starting point of deep learning-based reconstructions on non-cartesian trajectories. Further studies will focus on directly applying the deep learning networks to reconstruct images from the k-space with non-cartesian grids and larger under-sampling factors and how the reconstruction method affects group comparison results.

Acknowledgements

No acknowledgement found.

References

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