Tieyuan Lu^{1}, Xinlin Zhang^{1}, Yihui Huang^{1}, Di Guo^{2}, and Xiaobo Qu^{1}

^{1}Department of Electronic Science, Xiamen University, Xiamen, China, ^{2}School of Computer and Information Engineering, Xiamen University of Technology, Xiamen, China

Magnetic resonance imaging has been widely applied in clinical diagnosis, however, is limited by its long data acquisition time. Although imaging can be accelerated by sparse sampling and parallel imaging, achieving promising reconstruction images with a fast reconstruction speed remains a challenge. In this work, we design the neural network structure from the perspective of sparse iterative reconstruction. The experimental results of a public knee dataset show that compared with the optimization-based method and the latest deep learning parallel imaging methods, the proposed network has less error in reconstruction and is more stable under different acceleration factors.

Each update step of iteration in pISTA-SENSE is replaced by different operations or modules of an iteration block in our proposed pISTA-SENSE-ResNet, shown in Fig.1. However, the iteration blocks in network is fixed in a small number $$$S=10$$$ compared with the pISTA-SENSE.

The DC module in the $$${{s}^{th}}$$$ iteration block of our pISTA-SENSE-ResNet keeps same with the one in pISTA-SENSE, which is built to keep the data consistency between the acquired k-space $$${{\mathbf{y}}_{j}}$$$data and the predicted one $$${{\mathbf{x}}_{s}}$$$ by the network and formulated as: $${{\mathbf{t}}_{s}}={{\mathbf{x}}_{s}}+{{\gamma }_{s}}\sum\limits_{j=1}^{J}{\mathbf{C}_{j}^{H}{{\mathbf{F}}^{H}}{{\mathbf{U}}^{T}}\left( {{\mathbf{y}}_{j}}-\mathbf{UF}{{\mathbf{C}}_{j}}{{\mathbf{x}}_{s}} \right)}, (2)$$ where $$$\gamma $$$ is the step size, the superscript $$$H$$$and $$$T$$$ denote conjugate transpose and transpose respectively. Another module consists of three operations and adds a skip connection, inspired by the ResNet

Among these reconstruction results, pISTA-SENSE-ResNet recovers the image more close to the fully sampled images: first, some details are recovered faithfully, while others not, such as the red arrow pointed in Fig.2 and Fig.3, second, the excessively sharp edge are well suppressed as the green arrows pointed in Fig.3. Besides this, less error is observed at the reconstruction results of pISTA-SENSE-ResNet according to the error maps. As shown in the TABLE I, pISTA-SENSE-ResNet reaches the lowest mean value of RLNE and highest mean MSSIM, which means our method reaches the least average reconstruction error and the superior detail recovery among these methods.

This work was supported in part by National Key R&D Program of China (2017YFC0108703), National Natural Science Foundation of China (61571380, 61971361, 61871341, and 61811530021), Natural Science Foundation of Fujian Province of China (2018J06018), Fundamental Research Funds for the Central Universities (20720180056), Science and Technology Program of Xiamen (3502Z20183053), and China Scholarship Council. The authors would thank the GPU donated by NIVDIA Corporation.

The correspondence should be sent to Dr. Xiaobo Qu (Email: quxiaobo@xmu.edu.cn)

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Figure 1. The proposed
pISTA-SENSE-ResNet for parallel MRI reconstruction

Figure 2. Reconstruction results
comparison (AF = 7): (a) the fully sampled coil-combined image, (b-e) the
reconstruction of pFISTA-SENSE, VN, MoDL, and pISTA-SENSE-ResNet respectively,
(f) is the sampling pattern, (g-j) are the error maps of (b-e), respectively.

Figure 3. Reconstruction results
comparison (AF = 9): (a) the fully sampled coil-combined image, (b-e) the
reconstruction of pFISTA-SENSE, VN, MoDL, and pISTA-SENSE-ResNet respectively,
(f) is the sampling pattern, (g-j) are the error maps of (b-e), respectively.

Table 1. Objective criteria on the testing dataset. The
mean value and standard division are respect to the whole testing dataset under
certain method and acceleration factor (AF). And the average reconstruction
time per slice for each method is also attached in the last column