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Nonlocal latent low rank sparse representation for single image super resolution via self-similarity learning
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 |
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.
References:
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K. T. Block, M. Uecker and J. Frahm,
Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint, Magnetic Resonance in Medicine, 57 (2007), 1086-1098.
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[3] |
J. Caballero, A. N. Price, D. Rueckert and J. V Hajnal,
Dictionary learning and time sparsity for dynamic MR data reconstruction, IEEE Transactions on Medical Imaging, 33 (2014), 979-994.
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[4] |
L. Chaari, J. C. Pesquet, A. Benazza-Benyahia and P. Ciuciu,
A wavelet-based regularized reconstruction algorithm for SENSE parallel MRI with applications to neuroimaging, Med. Image Anal, 15 (2011), 185-201.
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[5] |
T. Eo, Y. Jun, T. Kim, J. Jang, H. Lee and D. Hwang,
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[6] |
K. Hammernik, T. Klatzer, E. Kobler, M. P. Recht, D. K. Sodickson, T. Pock and F. Knoll,
Learning a variational network for reconstruction of accelerated MRI data, Magnetic Resonance in Medicine, 79 (2018), 3055-3071.
doi: 10.1002/mrm.26977. |
[7] |
Y. Han, J. Yoo, H. H. Kim, H. J. Shin, K. Sung and J. C. Ye,
Deep learning with domain adaptation for accelerated projection–reconstruction MR, Magnetic Resonance in Medicine, 80 (2018), 1189-1205.
|
[8] |
H. Jung, K. Sung, K. S. Nayak, E. Y. Kim and J. C. Ye,
K-T FOCUSS: A general compressed sensing framework for high resolution dynamic MRI, Magnetic Resonance in Medicine. An Off. J. Int. Soc. Magn. Reson. Med, 61 (2009), 103-116.
|
[9] |
H. Jung, J. Yoo and J. C. Ye, Generalized kt BLAST and kt SENSE using FOCUSS, 2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro. IEEE, (2007), 145–148.
doi: 10.1109/ISBI.2007.356809. |
[10] |
H. Jung and J. C. Ye,
Motion estimated and compensated compressed sensing dynamic magnetic resonance imaging: What we can learn from video compression techniques, Int. J. Imaging Syst. Technol, 20 (2010), 81-98.
doi: 10.1002/ima.20231. |
[11] |
W. A. Kaiser and E. Zeitler,
MR imaging of the breast: Fast imaging sequences with and without Gd-DTPA. Preliminary observations, Radiology, 170 (1989), 681-686.
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[12] |
F. Knoll, T. Murrell, A. Sriram, N. Yakubova, J. Zbontar, M. Rabbat, A. Defazio, M. J. Muckley, D. K. Sodickson, C. L. Zitnick and M. P. Recht, Advancing machine learning for MR image reconstruction with an open competition: Overview of the 2019 fastMRI challenge, arXiv preprint, arXiv: 2001.02518, 2020. |
[13] |
D. Liang, J. Cheng and Z. Ke Z,
Deep magnetic resonance image reconstruction: Inverse problems meet neural networks, IEEE Signal Processing Magazine, 37 (2020), 141-151.
doi: 10.1109/MSP.2019.2950557. |
[14] |
D. Liang, E. V. R. DiBella, R. R. Chen and L. Ying,
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[15] |
S. G. Lingala, Y. Hu, E. Dibella and M. Jacob,
Accelerated dynamic MRI exploiting sparsity and low-rank structure: K-t SLR, IEEE Transactions on Medical Imaging, 30 (2011), 1042-1054.
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[16] |
Q. Liu, Q. Yang, H. Cheng, S. Wang, M. Zhang and D. Liang,
highly undersampled magnetic resonance imaging reconstruction using autoencoder priors, Magnetic Resonance in Medicine, 83 (2020), 322-336.
doi: 10.1002/mrm.27921. |
[17] |
F. Liu, D. Li, X. Jin, W. Qiu, Q. Xia and B. Sun,
Dynamic cardiac MRI reconstruction using motion aligned locally low rank tensor (MALLRT), Magnetic Resonance in Medicine, 66 (2020), 104-115.
doi: 10.1016/j.mri.2019.07.002. |
[18] |
Y. Liu, Q. Liu, M. Zhang, Q. Yang, S. Wang and D. Liang,
IFR-net: Iterative feature refinement net-work for compressed sensing MRI, IEEE Transactions on Computational Imaging, 6 (2019), 434-446.
doi: 10.1109/TCI.2019.2956877. |
[19] |
M. Lustig, J. M. Santos, D. L. Donoho and J. M. Pauly, KT sparse: high frame-rate dynamic magnetic resonance imaging exploiting spatio-temporal sparsity, U.S. Patent, 7 (2009), 183. |
[20] |
A. Majumdar,
Improved dynamic MRI reconstruction by exploiting sparsity and rank-deficiency, Magn. Reson. Imaging, 31 (2013), 789-795.
doi: 10.1016/j.mri.2012.10.026. |
[21] |
A. Majumdar, R. K. Ward and T. Aboulnasr,
Non-convex algorithm for sparse and low-rank recovery: Application to dynamic MRI reconstruction, Magn. Reson. Imaging, 31 (2013), 448-455.
doi: 10.1016/j.mri.2012.08.011. |
[22] |
A. Majumdar,
Improving synthesis and analysis prior blind compressed sensing with low-rank constraints for dynamic MRI reconstruction, Magn. Reson. Imaging, 33 (2015), 174-179.
doi: 10.1016/j.mri.2014.08.031. |
[23] |
S. Osher, M. Burger, D. Goldfarb, J. Xu and W. Yin,
An iterative regularization method for total variation-based image restoration, Multiscale Model. Simul, 4 (2005), 460-489.
doi: 10.1137/040605412. |
[24] |
R. Otazo, E. Cands and D. K. Sodickson,
Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components, Magnetic Resonance in Medicine, 73 (2015), 1125-1136.
doi: 10.1002/mrm.25240. |
[25] |
T. M. Quan, T. Nguyen-Duc and W.-K. Jeong,
Compressed sensing MRI reconstruction using a generative adversarial network with a cyclic loss, IEEE Transactions on Medical Imaging, 37 (2018), 1488-1497.
doi: 10.1109/TMI.2018.2820120. |
[26] |
C. Qin, J. Schlemper, J. Caballero, A. N. Price, J. V Hajnal and D. Rueckert,
Convolutional recurrent neural networks for dynamic MR image reconstruction, IEEE Transactions on Medical Imaging, 38 (2019), 280-290.
doi: 10.1109/TMI.2018.2863670. |
[27] |
M. Rizkinia and M. Okuda,
Evaluation of primal-dual splitting algorithm for MRI reconstruction using spatio-temporal structure Tensor and L1-2 norm, Makara Journal of Technology, 23 (2020), 126-130.
doi: 10.7454/mst.v23i3.3892. |
[28] |
D. k. Sodickson and W. J. Manning,
Simultaneous acquisition of spatial harmonics (SMASH): Fast imaging with radiofrequency coil arrays, Magnetic Resonance in Medicine, 38 (1997), 591-603.
doi: 10.1002/mrm.1910380414. |
[29] |
J. Schlemper, J. Caballero, J. V Hajnal, A. N. Price and D. Ruecker,
A deep cascade of convolutional neural networks for dynamic MR image reconstruction, IEEE Transactions on Medical Imaging, 37 (2018), 491-503.
doi: 10.1109/TMI.2017.2760978. |
[30] |
J. Sun, H. Li and Z. Xu, Deep ADMM-Net for compressive sensing MRI, Advances in Neural Information Processing Systems, (2016), 10–18. http://papers.nips.cc/paper/6406-deep-admm-net-for-compressive-sensing-mri. |
[31] |
L. Sun, Z. Fan, Y. Huang, X. Ding and J. Paisley, Compressed sensing MRI using a recursive dilated network, Thirty-Second AAAI Conference on Artificial Intelligence, (2018). http://www.columbia.edu/ jwp2128/Papers/SunFanetal2018.pdf |
[32] |
J. Tsao, P. Boesiger and K. P. Pruessmann,
k-t BLAST and k-t SENSE: Dynamic MRI With High Frame Rate Exploiting Spatiotemporal Correlations, Magnetic Resonance in Medicine, 50 (2003), 1031-1042.
doi: 10.1002/mrm.10611. |
[33] |
S. Wang, Y. Xia, Q. Liu, P. Dong and D. Feng,
Fenchel duality based dictionary learning for restoration of noisy images, IEEE Transactions on Image Processing, 22 (2013), 5214-5225.
doi: 10.1109/TIP.2013.2282900. |
[34] |
Y. Wang, Y. Zhou and L. Ying, Undersampled dynamic magnetic resonance imaging using patch-based spatiotemporal dictionaries, 2013 IEEE 10th International Symposium on Biomedical Imaging, (2013), 294–297.
doi: 10.1109/ISBI.2013.6556470. |
[35] |
S. Wang, Z. Ke, H. Cheng, S. Jia, Y. Leslie, H. Zheng and D. Liang, Dimension: Dynamic mr imaging with both k-space and spatial prior knowledge obtained via multi-supervised network training, NMR in Biomedicine, (2019), e4131.
doi: 10.1002/nbm.4131. |
[36] |
S. Wang, Z. Su, L. Ying, X. Peng, S. Zhu, F. Liang, D. Feng and D. Liang, Accelerating magnetic resonance imaging via deep learning, 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI), (2016).
doi: 10.1109/ISBI.2016.7493320. |
[37] |
S. Wang, H. Cheng, L. Ying, T. Xiao, Z. Ke, H. Zheng and D. Liang,
DeepcomplexMRI: Exploiting deep residual network for fast parallel MR imaging with complex convolution, Magnetic Resonance in Medicine, 68 (2020), 136-147.
doi: 10.1016/j.mri.2020.02.002. |
[38] |
Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli, Image quality assessment: From error visibility to structural similarity, IEEE Transactions on Image Processing, 13 (2004), 600–612. https://ece.uwaterloo.ca/ z70wang/publications/ssim.pdf
doi: 10.1109/TIP.2003.819861. |
[39] |
J. Yao, Z. Xu, X. Huang and J Huang, Accelerated dynamic MRI reconstruction with total variation and nuclear norm regularization, International Conference on Medical Image Computing and Computer-Assisted Intervention, (2015), 635–642.
doi: 10.1007/978-3-319-24571-3_76. |
[40] |
G. Yang, S. Yu and H. Dong,
DAGAN: Deep de-aliasing generative adversarial networks for fast compressed sensing MRI reconstruction, IEEE Transactions on Medical Imaging, 37 (2018), 1310-1321.
doi: 10.1109/TMI.2017.2785879. |
[41] |
Y. Yang, J. Sun, H. Li and Z Xu,
ADMM-CSNet: A deep learning approach for image compressive sensing, IEEE Transactions on Pattern Analysis and Machine Intelligence, 42 (2018), 521-538.
|
[42] |
B. Zhao, J. P. Haldar, A. G. Christodoulou and Z.-P. Liang,
Image reconstruction from highly undersampled (k, t)-space data with joint partial separability and sparsity constraints, IEEE Transactions on Medical Imaging, 31 (2012), 1809-1820.
doi: 10.1109/TMI.2012.2203921. |
[43] |
B. Zhu, J. Z. Liu, S. F. Cauley, B. R. Rosen and M. S. Rosen,
Image reconstruction by domain-transform manifold learning, Nature, 555 (2018), 487-492.
doi: 10.1038/nature25988. |
show all references
References:
[1] |
H. K. Aggarwal, M. P. Mani and M. Jacob,
Modl: Model-based deep learning architecture for inverse problems, IEEE Transactions on Medical Imaging, 38 (2018), 394-405.
doi: 10.1109/TMI.2018.2865356. |
[2] |
K. T. Block, M. Uecker and J. Frahm,
Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint, Magnetic Resonance in Medicine, 57 (2007), 1086-1098.
doi: 10.1002/mrm.21236. |
[3] |
J. Caballero, A. N. Price, D. Rueckert and J. V Hajnal,
Dictionary learning and time sparsity for dynamic MR data reconstruction, IEEE Transactions on Medical Imaging, 33 (2014), 979-994.
doi: 10.1109/TMI.2014.2301271. |
[4] |
L. Chaari, J. C. Pesquet, A. Benazza-Benyahia and P. Ciuciu,
A wavelet-based regularized reconstruction algorithm for SENSE parallel MRI with applications to neuroimaging, Med. Image Anal, 15 (2011), 185-201.
doi: 10.1016/j.media.2010.08.001. |
[5] |
T. Eo, Y. Jun, T. Kim, J. Jang, H. Lee and D. Hwang,
KIKI-Net: Cross-domain convolutional neural networks for reconstructing undersampled magnetic resonance images, Magnetic Resonance in Medicine, 80 (2018), 2188-2201.
doi: 10.1002/mrm.27201. |
[6] |
K. Hammernik, T. Klatzer, E. Kobler, M. P. Recht, D. K. Sodickson, T. Pock and F. Knoll,
Learning a variational network for reconstruction of accelerated MRI data, Magnetic Resonance in Medicine, 79 (2018), 3055-3071.
doi: 10.1002/mrm.26977. |
[7] |
Y. Han, J. Yoo, H. H. Kim, H. J. Shin, K. Sung and J. C. Ye,
Deep learning with domain adaptation for accelerated projection–reconstruction MR, Magnetic Resonance in Medicine, 80 (2018), 1189-1205.
|
[8] |
H. Jung, K. Sung, K. S. Nayak, E. Y. Kim and J. C. Ye,
K-T FOCUSS: A general compressed sensing framework for high resolution dynamic MRI, Magnetic Resonance in Medicine. An Off. J. Int. Soc. Magn. Reson. Med, 61 (2009), 103-116.
|
[9] |
H. Jung, J. Yoo and J. C. Ye, Generalized kt BLAST and kt SENSE using FOCUSS, 2007 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro. IEEE, (2007), 145–148.
doi: 10.1109/ISBI.2007.356809. |
[10] |
H. Jung and J. C. Ye,
Motion estimated and compensated compressed sensing dynamic magnetic resonance imaging: What we can learn from video compression techniques, Int. J. Imaging Syst. Technol, 20 (2010), 81-98.
doi: 10.1002/ima.20231. |
[11] |
W. A. Kaiser and E. Zeitler,
MR imaging of the breast: Fast imaging sequences with and without Gd-DTPA. Preliminary observations, Radiology, 170 (1989), 681-686.
doi: 10.1148/radiology.170.3.2916021. |
[12] |
F. Knoll, T. Murrell, A. Sriram, N. Yakubova, J. Zbontar, M. Rabbat, A. Defazio, M. J. Muckley, D. K. Sodickson, C. L. Zitnick and M. P. Recht, Advancing machine learning for MR image reconstruction with an open competition: Overview of the 2019 fastMRI challenge, arXiv preprint, arXiv: 2001.02518, 2020. |
[13] |
D. Liang, J. Cheng and Z. Ke Z,
Deep magnetic resonance image reconstruction: Inverse problems meet neural networks, IEEE Signal Processing Magazine, 37 (2020), 141-151.
doi: 10.1109/MSP.2019.2950557. |
[14] |
D. Liang, E. V. R. DiBella, R. R. Chen and L. Ying,
K-t ISD: Dynamic cardiac MR imaging using compressed sensing with iterative support detection, Magnetic Resonance in Medicine, 68 (2012), 41-53.
doi: 10.1002/mrm.23197. |
[15] |
S. G. Lingala, Y. Hu, E. Dibella and M. Jacob,
Accelerated dynamic MRI exploiting sparsity and low-rank structure: K-t SLR, IEEE Transactions on Medical Imaging, 30 (2011), 1042-1054.
doi: 10.1109/TMI.2010.2100850. |
[16] |
Q. Liu, Q. Yang, H. Cheng, S. Wang, M. Zhang and D. Liang,
highly undersampled magnetic resonance imaging reconstruction using autoencoder priors, Magnetic Resonance in Medicine, 83 (2020), 322-336.
doi: 10.1002/mrm.27921. |
[17] |
F. Liu, D. Li, X. Jin, W. Qiu, Q. Xia and B. Sun,
Dynamic cardiac MRI reconstruction using motion aligned locally low rank tensor (MALLRT), Magnetic Resonance in Medicine, 66 (2020), 104-115.
doi: 10.1016/j.mri.2019.07.002. |
[18] |
Y. Liu, Q. Liu, M. Zhang, Q. Yang, S. Wang and D. Liang,
IFR-net: Iterative feature refinement net-work for compressed sensing MRI, IEEE Transactions on Computational Imaging, 6 (2019), 434-446.
doi: 10.1109/TCI.2019.2956877. |
[19] |
M. Lustig, J. M. Santos, D. L. Donoho and J. M. Pauly, KT sparse: high frame-rate dynamic magnetic resonance imaging exploiting spatio-temporal sparsity, U.S. Patent, 7 (2009), 183. |
[20] |
A. Majumdar,
Improved dynamic MRI reconstruction by exploiting sparsity and rank-deficiency, Magn. Reson. Imaging, 31 (2013), 789-795.
doi: 10.1016/j.mri.2012.10.026. |
[21] |
A. Majumdar, R. K. Ward and T. Aboulnasr,
Non-convex algorithm for sparse and low-rank recovery: Application to dynamic MRI reconstruction, Magn. Reson. Imaging, 31 (2013), 448-455.
doi: 10.1016/j.mri.2012.08.011. |
[22] |
A. Majumdar,
Improving synthesis and analysis prior blind compressed sensing with low-rank constraints for dynamic MRI reconstruction, Magn. Reson. Imaging, 33 (2015), 174-179.
doi: 10.1016/j.mri.2014.08.031. |
[23] |
S. Osher, M. Burger, D. Goldfarb, J. Xu and W. Yin,
An iterative regularization method for total variation-based image restoration, Multiscale Model. Simul, 4 (2005), 460-489.
doi: 10.1137/040605412. |
[24] |
R. Otazo, E. Cands and D. K. Sodickson,
Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components, Magnetic Resonance in Medicine, 73 (2015), 1125-1136.
doi: 10.1002/mrm.25240. |
[25] |
T. M. Quan, T. Nguyen-Duc and W.-K. Jeong,
Compressed sensing MRI reconstruction using a generative adversarial network with a cyclic loss, IEEE Transactions on Medical Imaging, 37 (2018), 1488-1497.
doi: 10.1109/TMI.2018.2820120. |
[26] |
C. Qin, J. Schlemper, J. Caballero, A. N. Price, J. V Hajnal and D. Rueckert,
Convolutional recurrent neural networks for dynamic MR image reconstruction, IEEE Transactions on Medical Imaging, 38 (2019), 280-290.
doi: 10.1109/TMI.2018.2863670. |
[27] |
M. Rizkinia and M. Okuda,
Evaluation of primal-dual splitting algorithm for MRI reconstruction using spatio-temporal structure Tensor and L1-2 norm, Makara Journal of Technology, 23 (2020), 126-130.
doi: 10.7454/mst.v23i3.3892. |
[28] |
D. k. Sodickson and W. J. Manning,
Simultaneous acquisition of spatial harmonics (SMASH): Fast imaging with radiofrequency coil arrays, Magnetic Resonance in Medicine, 38 (1997), 591-603.
doi: 10.1002/mrm.1910380414. |
[29] |
J. Schlemper, J. Caballero, J. V Hajnal, A. N. Price and D. Ruecker,
A deep cascade of convolutional neural networks for dynamic MR image reconstruction, IEEE Transactions on Medical Imaging, 37 (2018), 491-503.
doi: 10.1109/TMI.2017.2760978. |
[30] |
J. Sun, H. Li and Z. Xu, Deep ADMM-Net for compressive sensing MRI, Advances in Neural Information Processing Systems, (2016), 10–18. http://papers.nips.cc/paper/6406-deep-admm-net-for-compressive-sensing-mri. |
[31] |
L. Sun, Z. Fan, Y. Huang, X. Ding and J. Paisley, Compressed sensing MRI using a recursive dilated network, Thirty-Second AAAI Conference on Artificial Intelligence, (2018). http://www.columbia.edu/ jwp2128/Papers/SunFanetal2018.pdf |
[32] |
J. Tsao, P. Boesiger and K. P. Pruessmann,
k-t BLAST and k-t SENSE: Dynamic MRI With High Frame Rate Exploiting Spatiotemporal Correlations, Magnetic Resonance in Medicine, 50 (2003), 1031-1042.
doi: 10.1002/mrm.10611. |
[33] |
S. Wang, Y. Xia, Q. Liu, P. Dong and D. Feng,
Fenchel duality based dictionary learning for restoration of noisy images, IEEE Transactions on Image Processing, 22 (2013), 5214-5225.
doi: 10.1109/TIP.2013.2282900. |
[34] |
Y. Wang, Y. Zhou and L. Ying, Undersampled dynamic magnetic resonance imaging using patch-based spatiotemporal dictionaries, 2013 IEEE 10th International Symposium on Biomedical Imaging, (2013), 294–297.
doi: 10.1109/ISBI.2013.6556470. |
[35] |
S. Wang, Z. Ke, H. Cheng, S. Jia, Y. Leslie, H. Zheng and D. Liang, Dimension: Dynamic mr imaging with both k-space and spatial prior knowledge obtained via multi-supervised network training, NMR in Biomedicine, (2019), e4131.
doi: 10.1002/nbm.4131. |
[36] |
S. Wang, Z. Su, L. Ying, X. Peng, S. Zhu, F. Liang, D. Feng and D. Liang, Accelerating magnetic resonance imaging via deep learning, 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI), (2016).
doi: 10.1109/ISBI.2016.7493320. |
[37] |
S. Wang, H. Cheng, L. Ying, T. Xiao, Z. Ke, H. Zheng and D. Liang,
DeepcomplexMRI: Exploiting deep residual network for fast parallel MR imaging with complex convolution, Magnetic Resonance in Medicine, 68 (2020), 136-147.
doi: 10.1016/j.mri.2020.02.002. |
[38] |
Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli, Image quality assessment: From error visibility to structural similarity, IEEE Transactions on Image Processing, 13 (2004), 600–612. https://ece.uwaterloo.ca/ z70wang/publications/ssim.pdf
doi: 10.1109/TIP.2003.819861. |
[39] |
J. Yao, Z. Xu, X. Huang and J Huang, Accelerated dynamic MRI reconstruction with total variation and nuclear norm regularization, International Conference on Medical Image Computing and Computer-Assisted Intervention, (2015), 635–642.
doi: 10.1007/978-3-319-24571-3_76. |
[40] |
G. Yang, S. Yu and H. Dong,
DAGAN: Deep de-aliasing generative adversarial networks for fast compressed sensing MRI reconstruction, IEEE Transactions on Medical Imaging, 37 (2018), 1310-1321.
doi: 10.1109/TMI.2017.2785879. |
[41] |
Y. Yang, J. Sun, H. Li and Z Xu,
ADMM-CSNet: A deep learning approach for image compressive sensing, IEEE Transactions on Pattern Analysis and Machine Intelligence, 42 (2018), 521-538.
|
[42] |
B. Zhao, J. P. Haldar, A. G. Christodoulou and Z.-P. Liang,
Image reconstruction from highly undersampled (k, t)-space data with joint partial separability and sparsity constraints, IEEE Transactions on Medical Imaging, 31 (2012), 1809-1820.
doi: 10.1109/TMI.2012.2203921. |
[43] |
B. Zhu, J. Z. Liu, S. F. Cauley, B. R. Rosen and M. S. Rosen,
Image reconstruction by domain-transform manifold learning, Nature, 555 (2018), 487-492.
doi: 10.1038/nature25988. |









2X | 3X | 4X | 5X | 7X | 9X | 11X | 2X | 3X | 4X | 5X | 7X | 9X | 11X | 15X |
2X | 3X | 4X | 5X | 7X | 9X | 11X | 2X | 3X | 4X | 5X | 7X | 9X | 11X | 15X |
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 |
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 |
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 |
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 |
Methods | Random 7X | Random 11X | ||||
PSNR | SSIM | HFEN | PSNR | SSIM | HFEN | |
Zero-filling | 29.14 |
0.57 |
2.73 |
27.58 |
0.51 |
3.12 |
Kt-SLR | 33.50 |
0.77 |
1.83 |
32.44 |
0.73 |
2.01 |
D5C5 | 36.76 |
0.78 |
1.40 |
35.22 |
0.73 |
1.82 |
Proposed | 37.48 |
0.82 |
1.31 |
35.40 |
0.77 |
1.67 |
Methods | Random 7X | Random 11X | ||||
PSNR | SSIM | HFEN | PSNR | SSIM | HFEN | |
Zero-filling | 29.14 |
0.57 |
2.73 |
27.58 |
0.51 |
3.12 |
Kt-SLR | 33.50 |
0.77 |
1.83 |
32.44 |
0.73 |
2.01 |
D5C5 | 36.76 |
0.78 |
1.40 |
35.22 |
0.73 |
1.82 |
Proposed | 37.48 |
0.82 |
1.31 |
35.40 |
0.77 |
1.67 |
Methods | Radial 11X | Radial 15X | ||||
PSNR/dB | SSIM | HFEN | PSNR/dB | SSIM | HFEN | |
Zero-filling | 22.269 |
0.345 |
5.198 |
20.153 |
0.275 |
5.986 |
Kt-SLR | 31.961 |
0.718 |
2.179 |
31.518 |
0.707 |
2.229 |
D5C5 | 34.954 |
0.701 |
1.735 |
34.248 |
0.677 |
1.907 |
Proposed | 38.874 |
0.831 |
1.019 |
38.115 |
0.808 |
1.164 |
Methods | Radial 11X | Radial 15X | ||||
PSNR/dB | SSIM | HFEN | PSNR/dB | SSIM | HFEN | |
Zero-filling | 22.269 |
0.345 |
5.198 |
20.153 |
0.275 |
5.986 |
Kt-SLR | 31.961 |
0.718 |
2.179 |
31.518 |
0.707 |
2.229 |
D5C5 | 34.954 |
0.701 |
1.735 |
34.248 |
0.677 |
1.907 |
Proposed | 38.874 |
0.831 |
1.019 |
38.115 |
0.808 |
1.164 |
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