LANTERN: Learn analysis transform network for dynamic magnetic resonance imaging

Shanshan Wang; Yanxia Chen; Taohui Xiao; Lei Zhang; Xin Liu; Hairong Zheng

doi:10.3934/ipi.2020051

Article Contents

2021, Volume 15, Issue 6: 1363-1379. Doi: 10.3934/ipi.2020051 open access

This issue Previous Article Nonlocal latent low rank sparse representation for single image super resolution via self-similarity learning Next Article Image retinex based on the nonconvex TV-type regularization

LANTERN: Learn analysis transform network for dynamic magnetic resonance imaging

1.
Paul C. Lauterbur Research Center for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, Guangdong, China, 1068 Xueyuan Avenue, Shenzhen University Town, Shenzhen, China
2.
University of Chinese Academy of Sciences, Beijing, China, 19 Yuquan Road, Shijingshan District, Beijing, China

^* Corresponding author: Hairong Zheng
^* Corresponding author: Hairong Zheng

S. Wang and Y. Chen contributed equally to this work

Received: November 30, 2019

Revised: April 30, 2020

Early access: August 2020

Published: December 2021

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Abstract

This paper proposes to learn analysis transform network for dynamic magnetic resonance imaging (LANTERN). Integrating the strength of CS-MRI and deep learning, the proposed framework is highlighted in three components: (ⅰ) The spatial and temporal domains are sparsely constrained by adaptively trained convolutional filters; (ⅱ) We introduce an end-to-end framework to learn the parameters in LANTERN to solve the difficulty of parameter selection in traditional methods; (ⅲ) Compared to existing deep learning reconstruction methods, our experimental results show that our paper has encouraging capability in exploiting the spatial and temporal redundancy of dynamic MR images. We performed quantitative and qualitative analysis of cardiac reconstructions at different acceleration factors ($ 2 \times $-$ 11 \times $) with different undersampling patterns. In comparison with two state-of-the-art methods, experimental results show that our method achieved encouraging performances.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. The proposed LANTERN network architecture for dMRI reconstruction. In (A) and (B), the blue arrow indicates forward process. The pink arrow indicates the process of back-propagation to update network parameters, where $ i $ represents the $ i - th $ iteration and $ N_i $ represents a total of $ N_i $ iterations. $ k $ expresses that the priori loop for $ k $ times and $ (i, k) $ means that in the $ i-th $ iteration, the a priori loops $ k $ times

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Figure 2. Visual results comparison for the sensitivity to the training data size. From left to right, the reconstruction results (top line) with neural networks trained from different amounts of data based on the proposed method with 1D random sampling pattern at an acceleration factor of 4. PSNR values are given in the middle and the reconstruction error maps are presented at the bottom

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Figure 3. The comparison of the three initialization modes of Random Gaussian, TV, DCT and LANTERN based on the proposed method with 1D Random sampling at an acceleration factor of 4. PSNR value are given under the results

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Figure 4. The comparison of k-t SLR, D5C5 and the proposed method with 1D Random sampling at an acceleration factor of 4. PSNR value is given under the results

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Figure 5. The comparison of k-t SLR, D5C5 and the proposed method with 1D Random sampling at an acceleration factor of 5. PSNR value is given under the results

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Figure 6. The comparison of various methods between average quantification index of the 50 test data and acceleration factor based on 1D Random sampling

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Figure 8. The comparison of various methods between average quantification index of the 50 test data and acceleration factor based on Radial sampling

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Figure 9. The training and validation loss curves of the proposed model

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Figure 7. The comparison of k-t SLR, D5C5 and the proposed method with 2D Radial sampling at an acceleration factor of 11. PSNR value is given under the results

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Table 1. Experimental masks and acceleration factors

$\bf{1D\ Random}$							$\bf{2D\ Radial}$
2X	3X	4X	5X	7X	9X	11X	2X	3X	4X	5X	7X	9X	11X	15X

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Table 2. Quantitative results comparison for the sensitivity to the training data size. The average quantitative indicator values of the results reconstructed for the 50 test data with the network trained from different different amount of data with 1D Random sampling pattern at an accelerated factor of 4

1D Random4x	NMSE	PSNR/dB	SSIM	HFEN
data50	0.0413	40.8047	0.8943	0.8333
data60	0.0397	41.1515	0.9	0.7939
data80	0.0388	41.3589	0.9034	0.7729
data100	0.0385	41.4391	0.9043	0.7633
data120	0.0386	41.4402	0.9035	0.7685

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Table 3. Quantitative results comparison for the sensitivity to the initialization. The average quantitative indicator values of the results reconstructed for the 50 test data with the network trained with different initialization with 1D Random sampling pattern at an accelerated factor of 4

1D Random4x	Gaussian		TV		DCT		LANTERN
	PSNR	HFEN	PSNR	HFEN	PSNR	HFEN	PSNR	HFEN
AVE	39.8089	0.9459	40.5884	0.8514	40.9971	0.8064	41.4391	0.7633

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Table 4. Average reconstruction quantitative metrics with standard deviation of the 50 test data based on various methods with 1D Random sampling at a different accelerated factor

Methods	Random 7X			Random 11X
	PSNR	SSIM	HFEN	PSNR	SSIM	HFEN
Zero-filling	29.14$ \pm $2.2	0.57$ \pm $0.04	2.73$ \pm $0.65	27.58$ \pm $2.08	0.51$ \pm $0.04	3.12$ \pm $0.74
Kt-SLR	33.50$ \pm $2.70	0.77$ \pm $0.03	1.83$ \pm $0.53	32.44$ \pm $2.61	0.73$ \pm $0.03	2.01$ \pm $0.63
D5C5	36.76$ \pm $2.00	0.78$ \pm $0.03	1.40$ \pm $0.33	35.22$ \pm $2.00	0.73$ \pm $0.03	1.82$ \pm $0.50
Proposed	37.48$ \pm $2.45	0.82$ \pm $0.02	1.31$ \pm $0.36	35.40$ \pm $2.60	0.77$ \pm $0.03	1.67$ \pm $0.53

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Table 5. Average reconstruction quantitative metrics with standard deviation of the 50 test data based on various methods with radial sampling at a different accelerated factor

Methods	Radial 11X		Radial 15X
	PSNR/dB	SSIM	HFEN	PSNR/dB	SSIM	HFEN
Zero-filling	22.269$ \pm $1.37	0.345$ \pm $0.06	5.198$ \pm $0.72	20.153$ \pm $1.27	0.275$ \pm $0.05	5.986$ \pm $0.67
Kt-SLR	31.961$ \pm $2.34	0.718$ \pm $0.03	2.179$ \pm $0.51	31.518$ \pm $2.36	0.707$ \pm $0.04	2.229$ \pm $0.54
D5C5	34.954$ \pm $2.08	0.701$ \pm $0.03	1.735$ \pm $0.42	34.248$ \pm $2.04	0.677$ \pm $0.03	1.907$ \pm $0.45
Proposed	38.874$ \pm $2.28	0.831$ \pm $0.03	1.019$ \pm $0.26	38.115$ \pm $2.23	0.808$ \pm $0.03	1.164$ \pm $0.30

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