##
**LANTERN: learn analysis transform network for dynamic magnetic resonance imaging.**
*(English)*
Zbl 1480.78013

Summary: 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.

### MSC:

78A46 | Inverse problems (including inverse scattering) in optics and electromagnetic theory |

78A70 | Biological applications of optics and electromagnetic theory |

78-05 | Experimental work for problems pertaining to optics and electromagnetic theory |

78M50 | Optimization problems in optics and electromagnetic theory |

65K10 | Numerical optimization and variational techniques |

65T50 | Numerical methods for discrete and fast Fourier transforms |

68T07 | Artificial neural networks and deep learning |

92C55 | Biomedical imaging and signal processing |

68U10 | Computing methodologies for image processing |

PDF
BibTeX
XML
Cite

\textit{S. Wang} et al., Inverse Probl. Imaging 15, No. 6, 1363--1379 (2021; Zbl 1480.78013)

Full Text:
DOI

### References:

[1] | H. K. Aggarwal; M. P. Mani; M. Jacob, Modl: Model-based deep learning architecture for inverse problems, IEEE Transactions on Medical Imaging, 38, 394-405 (2018) |

[2] | K. T. Block; M. Uecker; J. Frahm, Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint, Magnetic Resonance in Medicine, 57, 1086-1098 (2007) |

[3] | J. Caballero; A. N. Price; D. Rueckert; J. V. Hajnal, Dictionary learning and time sparsity for dynamic MR data reconstruction, IEEE Transactions on Medical Imaging, 33, 979-994 (2014) |

[4] | L. Chaari; J. C. Pesquet; A. Benazza-Benyahia; P. Ciuciu, A wavelet-based regularized reconstruction algorithm for SENSE parallel MRI with applications to neuroimaging, Med. Image Anal, 15, 185-201 (2011) |

[5] | T. Eo; Y. Jun; T. Kim; J. Jang; H. Lee; D. Hwang, KIKI-Net: Cross-domain convolutional neural networks for reconstructing undersampled magnetic resonance images, Magnetic Resonance in Medicine, 80, 2188-2201 (2018) |

[6] | K. Hammernik; T. Klatzer; E. Kobler; M. P. Recht; D. K. Sodickson; T. Pock; F. Knoll, Learning a variational network for reconstruction of accelerated MRI data, Magnetic Resonance in Medicine, 79, 3055-3071 (2018) |

[7] | Y. Han; J. Yoo; H. H. Kim; H. J. Shin; K. Sung; J. C. Ye, Deep learning with domain adaptation for accelerated projection-reconstruction MR, Magnetic Resonance in Medicine, 80, 1189-1205 (2018) |

[8] | H. Jung; K. Sung; K. S. Nayak; E. Y. Kim; 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, 103-116 (2009) |

[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. |

[10] | H. Jung; 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, 81-98 (2010) |

[11] | W. A. Kaiser; E. Zeitler, MR imaging of the breast: Fast imaging sequences with and without Gd-DTPA. Preliminary observations, Radiology, 170, 681-686 (1989) |

[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; Z. Ke Z., Deep magnetic resonance image reconstruction: Inverse problems meet neural networks, IEEE Signal Processing Magazine, 37, 141-151 (2020) |

[14] | D. Liang; E. V. R. DiBella; R. R. Chen; L. Ying, K-t ISD: Dynamic cardiac MR imaging using compressed sensing with iterative support detection, Magnetic Resonance in Medicine, 68, 41-53 (2012) |

[15] | S. G. Lingala; Y. Hu; E. Dibella; M. Jacob, Accelerated dynamic MRI exploiting sparsity and low-rank structure: K-t SLR, IEEE Transactions on Medical Imaging, 30, 1042-1054 (2011) |

[16] | Q. Liu; Q. Yang; H. Cheng; S. Wang; M. Zhang; D. Liang, highly undersampled magnetic resonance imaging reconstruction using autoencoder priors, Magnetic Resonance in Medicine, 83, 322-336 (2020) |

[17] | F. Liu; D. Li; X. Jin; W. Qiu; Q. Xia; B. Sun, Dynamic cardiac MRI reconstruction using motion aligned locally low rank tensor (MALLRT), Magnetic Resonance in Medicine, 66, 104-115 (2020) |

[18] | Y. Liu; Q. Liu; M. Zhang; Q. Yang; S. Wang; D. Liang, IFR-net: Iterative feature refinement net-work for compressed sensing MRI, IEEE Transactions on Computational Imaging, 6, 434-446 (2019) |

[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, 789-795 (2013) |

[21] | A. Majumdar; R. K. Ward; T. Aboulnasr, Non-convex algorithm for sparse and low-rank recovery: Application to dynamic MRI reconstruction, Magn. Reson. Imaging, 31, 448-455 (2013) |

[22] | A. Majumdar, Improving synthesis and analysis prior blind compressed sensing with low-rank constraints for dynamic MRI reconstruction, Magn. Reson. Imaging, 33, 174-179 (2015) |

[23] | S. Osher; M. Burger; D. Goldfarb; J. Xu; W. Yin, An iterative regularization method for total variation-based image restoration, Multiscale Model. Simul, 4, 460-489 (2005) · Zbl 1090.94003 |

[24] | R. Otazo; E. Cands; 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, 1125-1136 (2015) |

[25] | T. M. Quan; T. Nguyen-Duc; W.-K. Jeong, Compressed sensing MRI reconstruction using a generative adversarial network with a cyclic loss, IEEE Transactions on Medical Imaging, 37, 1488-1497 (2018) |

[26] | C. Qin; J. Schlemper; J. Caballero; A. N. Price; J. V. Hajnal; D. Rueckert, Convolutional recurrent neural networks for dynamic MR image reconstruction, IEEE Transactions on Medical Imaging, 38, 280-290 (2019) |

[27] | M. Rizkinia; 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, 126-130 (2020) |

[28] | D. k. Sodickson; W. J. Manning, Simultaneous acquisition of spatial harmonics (SMASH): Fast imaging with radiofrequency coil arrays, Magnetic Resonance in Medicine, 38, 591-603 (1997) |

[29] | J. Schlemper; J. Caballero; J. V. Hajnal; A. N. Price; D. Ruecker, A deep cascade of convolutional neural networks for dynamic MR image reconstruction, IEEE Transactions on Medical Imaging, 37, 491-503 (2018) |

[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; K. P. Pruessmann, k-t BLAST and k-t SENSE: Dynamic MRI With High Frame Rate Exploiting Spatiotemporal Correlations, Magnetic Resonance in Medicine, 50, 1031-1042 (2003) |

[33] | S. Wang; Y. Xia; Q. Liu; P. Dong; D. Feng, Fenchel duality based dictionary learning for restoration of noisy images, IEEE Transactions on Image Processing, 22, 5214-5225 (2013) · Zbl 1373.94431 |

[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. |

[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. |

[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). |

[37] | S. Wang; H. Cheng; L. Ying; T. Xiao; Z. Ke; H. Zheng; D. Liang, DeepcomplexMRI: Exploiting deep residual network for fast parallel MR imaging with complex convolution, Magnetic Resonance in Medicine, 68, 136-147 (2020) |

[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 |

[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. |

[40] | G. Yang; S. Yu; H. Dong, DAGAN: Deep de-aliasing generative adversarial networks for fast compressed sensing MRI reconstruction, IEEE Transactions on Medical Imaging, 37, 1310-1321 (2018) |

[41] | Y. Yang; J. Sun; H. Li; Z. Xu, ADMM-CSNet: A deep learning approach for image compressive sensing, IEEE Transactions on Pattern Analysis and Machine Intelligence, 42, 521-538 (2018) |

[42] | B. Zhao; J. P. Haldar; A. G. Christodoulou; 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, 1809-1820 (2012) |

[43] | B. Zhu; J. Z. Liu; S. F. Cauley; B. R. Rosen; M. S. Rosen, Image reconstruction by domain-transform manifold learning, Nature, 555, 487-492 (2018) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.