Synopsis

A permanent magnet based low-field MRI system provides portability and affordability. However, the quality of the image is low due to a low signal-to-noise ratio (SNR). We propose a new deep learning structure which effectively integrates denoising-networks end-to-end to super-resolution-networks, to transfer the rich information available from one-off experimental imaging from a mid-field MRI scanner (1.5T) to the lower-quality data from a portable system. The procedure uses matched pairs to learn mappings from low-quality to the corresponding high-quality images. Using the proposed method, the quality and resolution of an image from a low-field MRI system is significantly improved.

INTRODUCTION

Low-field MRI systems using permanent magnet arrays offer portability with affordability[1-2]. However, the field strength is relatively low which results in a low signal-to-noise ratio (SNR), and thus a low image quality. Here, we propose a new deep learning structure, which effectively integrates denoising-networks end-to-end to super-resolution-networks, to transfer the rich information available from one-off experimental imaging from mid-field MRI scanners (1.5T) to the lower-quality data from portable systems. We propose to use matched pairs to learn mappings from low-quality to the corresponding high-quality images.

Deep-neural-network(DNN) has been applied to single-image super-resolution[3-9]. A direct application of super-resolution on noisy images leads to inevitable magnified noises and distortions. Denoising is necessary before super-resolving images. In[10], convolutional-neural-network(CNN) was used to yield residuals, obtaining superior performance over other denoisers. End-to-end networks for jointly denoising and super-resolution were applied to restore natural images[11]. However, they are complexed and computationally expensive. For MRI images, the diversity between an image-pair is low, and it allows multiple scans of the same subject. The available networks are unnecessarily complicated, which could result in non-convergence or overfitting to training data.

MATERIALS & METHODS

We propose a simpler and more targeted model (shown in Fig.1(a)) for a quality transformation of low-field MRI images. It consists of a denoising-branch with 10 denoising-blocks and a super-resolution-branch with 16 super-resolution-blocks, bridged by a transpose-convolutional-layer. The number of parameters is half of that of EDSR[9]. A loss function in (1) (Fig.1(b)) which consists of a denoising-term and a super-resolution-term was used to drive the learning. Term-1 is the weighted difference of the low-resolution noise-free-image, $$$\hat{I}_{LR}$$$ ($$$\hat{I}_{LR}=I_N-\hat{N}$$$, at the exit of denoising-branch), and the $$$r$$$-time down-sampled high-quality image, $$$I_{HR/r}$$$.

In Fig.1(a), each denoising-branch consists of two convolutions, two batch-normalization, an activation function (rectified-linear-unit (ReLU)), and an element-wise summation, with the size of convolution kernel, stride, and padding labeled. Instead of explicitly calculating the noise-residual of images[10], a long skip-connection was used as the residual-yielding-process internally to obtain $$$\hat{I}_{LR}$$$. Thus, the networks can be trained through Term-1 in (1) using intermedium-predicted images rather than noise patterns. In Fig.1(a), following the denoising-branch, transpose-convolutional-layer up-samples the matrix $$$r$$$-time for further super-revolving. The super-resolution-branch is similar to the denoising-branch without batch-normalization because batch-normalization does not favor super-resolving fine features or maintain original contrast levels[9]. Skip-connection was applied to this branch. Super-resolution-branch outputs $$$\hat{I}_{r\times}$$$ and the difference between $$$\hat{I}_{r\times}$$$ and the high-quality image, $$$\hat{I}_{HR}$$$, forms Term-2 in (1).

To train the network, 1000 high-quality images (1.5T, Siemens, $$$240\times 240$$$pixels) were downloaded[12] and the corresponding low-field low-quality images were generated based on the Halbach-array-based low-field MRI system (68mT)[2]. An encoding term, $$$C_q(\mathbf{r})e^{-i2\pi\gamma\mathbf{B_0}t}$$$, was used from the signal equation $$$S_q(t)=\int_VC_q(\mathbf{r})e^{-i2\pi\gamma\mathbf{B_0}t}m(\mathbf{r})d\mathbf{r}$$$ to generate low-field images where $$$C_q(\mathbf{r})$$$ is the sensitivity of the $$$q^{th}$$$ coil, $$$\mathbf{B_0}$$$ is the spatial encoding magnetic field. The resolution of the image is determined by the pattern of $$$\mathbf{B_0}$$$[13]. It is down-sampled $$$r$$$-time. Gaussian-white-noise with a deviation of $$$\sigma_\textrm{sigma}$$$ was added to the signal to obtain noisy images. When $$$\sigma_\textrm{sigma}=-20$$$dB, the standard deviation of the noise-residual-image ($$$\sigma$$$) is 0.1. Both the high-quality images (Fig.2(a)) and the noisy low-resolution ones (Fig.2(b)) from the low-field system were fed to the network for training.

RESULTS

DISCUSSION & CONCLUSION

Acknowledgements

References