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An Unsupervised Deep Learning Approach for Reconstructing Arterial Spin Labeling Images from Noisy Data
Kuang Gong1, Paul Kyu Han1, Debra E. Horng1, Georges El Fakhri1, Chao Ma1, and Quanzheng Li1

1Gordon Center for Medical Imaging, Massachusetts General Hospital and Harvard Medical School, Boston, MA, United States

### Synopsis

Recently convolutional neural networks (CNNs) have been successfully applied to computer vision tasks and attracted growing interests in medical imaging. One barrier for the application of deep neural networks is the need of large amounts of training pairs, which are not always available in clinical practice. Inspired by the deep image prior method, this work presents a new image reconstruction framework based on CNN representation where no training pairs and pre-training are needed. We demonstrate the effectiveness of the proposed method by performing denoising and image reconstruction using noisy arterial spin labeling (ASL) data with and without undersampling.

### Introduction

Convolutional neural networks (CNNs) have achieved great success in computer vision, and currently been applied to medical image denoising and reconstruction tasks [1-11]. One requirement for the successful application of CNN is large amount of training pairs. In applications such as 3D cardiac magnetic resonance (MR) imaging, labels reconstructed from free-breathing fully-sampled data is difficult to get. For image reconstruction tasks, raw k-space data is needed but not easy to collect retrospectively.

Recently, it is shown in the deep image prior framework that CNN can learn intrinsic structures from corrupted images and is possible to restore the clean image from its corrupted version by only employing random noise as network input [12]. Different from natural images, for MR scans, prior images of the same subject, instead of random noise, can be employed as network input, which should further improve the results. Furthermore, instead of using the corrupted image as training labels, k-space data can be utilized as training labels and the training objective function can be formulated based on maximum likelihood.

Inspired by these two observations, we propose a new image reconstruction framework using CNN as image representation. The CNN is trained from scratch along with the reconstruction and no prior training data are needed. The proposed framework can be advantageous in applications such as arterial spin labeling (ASL) imaging [13,14], where the perfusion signal suffers from inherently low signal-to-noise ratio (SNR) [15,16], while the control image has high SNR and can be used as network input. Performance of the proposed method is tested using denoising and undersampled reconstruction cases.

### Methods

The unknown magnitude image $x$ is represented by a CNN output: $$x = f(\theta|z),$$ where $f:\mathbb{R}\rightarrow\mathbb{R}, \theta, z$ indicate the CNN, network trainable parameters and network input, respectively. A modified 3D U-net [17] shown in Fig. 1 is used as the network structure. As proof-of-concept, we choose the control image of ASL as the network input $z$. For denoising applications, the training function is L2 norm of the difference between the network output and the noisy image: $$\hat{\theta} = \underset{\theta}{\operatorname{argmin}} ||f(\theta | z) - b||_2,$$ where $b$ denotes the noisy magnitude image. For image reconstruction from undersampled k-space data using the SENSE framework [18], the training function is constructed as $$\hat{\theta} =\underset{\theta}{\operatorname{argmin}} ||\Omega FSPf(\theta | z) - d||_2 + \lambda ||f(\theta | z)||_2,$$ where $\Omega, F, P, d$ denotes down-sampling mask, Fourier transform, coil sensitivity maps, phase information matrix and k-space data, respectively. As the system matrix is coupled with the neural network, alternating direction method of multipliers (ADMM) [19] (details shown in Fig. 2) is used to separate the reconstruction and network training steps as the network training need more updates. In addition, ADMM allows the direct use of penalized image reconstruction methods at the image reconstruction step, which have been extensively studied with many existing packages and toolboxes. L-BFGS [20] is chosen as the network training algorithm due to its monotonic property. PCG algorithm [21] is used to solve the penalized reconstruction. For each loop the network training step was run 20 epochs and in total 100 outer-iterations were run.

All experiments were performed on a healthy subject using a 3T whole-body MR scanner approved by our local IRB. All ASL images were acquired using pseudo-continuous ASL (pCASL) [22,23] with balanced steady-state free precession readout [24,25]. The pCASL labeling parameters were as follows: flip angle=25°; RF duration/space =0.5/0.92 ms; total tagging duration=1500 ms, PLD time=1.2 s. Imaging parameters were as follows: FOV=240x180x120 mm3; encoding matrix size = 128x96x24, TR/TE=3.96/1.74 ms; total acquisition time=~5.3 min. For the undersampling case, 25% of each repetition was used (4x down-sampling). Signal-to-noise ratio (SNR) was calculated as the mean of the perfusion subtraction signal in the gray matter region divided by the standard deviation of noise.

### Results

Fig 3. Shows the image denoising results obtained by the proposed method, which were also compared with nonlocal-mean (NLM) [26] and guided filter methods [27]. We can see that the proposed method can reveal more cortex details than the compared methods. SNR values shown in Table 1 of Fig. 5 confirms this observation. Fig 4 shows the reconstructed images using 25% of k-space data for each repetition. Compared with the method including NLM in the reconstruction framework [28], the proposed method produced images with superior quality. Table 2 of Fig.5 confirms this observation.

### Conclusions

We propose a new reconstruction framework by representing the unknown image as CNN output. Prior training pairs are not needed, but only the subject’s own images from other sequences. Results of both image denoising and reconstruction from undersampled data demonstrate the superior performance of the proposed framework.

### Acknowledgements

This work was supported by NIH grants R01 AG052653 and P41 EB022544.

### References

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### Figures

The schematic plot of the modified 3D Unet structure used in this work. The spatial input size for each layer is based on the ASL image size. Compared to the original Unet, (1) pooling layer is replaced by convolutional layer with stride 2 to construct a fully convolutional network; (2) deconvolutional layer is replaced by a bilinear interpretation layer to reduce checkboard artifact; (3) concatenating layer is replaced by the adding layer to reduce trainable parameters.

The flowchart of the proposed ADMM algorithm for under-sampling reconstruction.

The denoising results using different method. The first row presents the noisy ASL images. The second row shows the denoising results using the proposed method. The third row shows the denoising results using the nonlocal-mean (NLM) filter (patch size 3 x 3 x 3, searching window size 7 x 7 x 7). The last row shows the denoising results using the image-guided filter.

The reconstruction results using different method for the down-sampling case (4x down-sampling). The first row presents the fully sampled ASL images. The second row show the noisy down-sampled data (4 times down-sampling). The third row shows the reconstruction results using the proposed method using down-sampled data. The fourth row shows the reconstruction results by including the nonlocal-mean (NLM) filter into the system model.

Table 1 shows the SNR values for different denoising methods based on the fully sampled data. Table 2 shows the SNR values for different reconstruction methods based on the under-sampled data (4x down-sampling).

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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