{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:25:31Z","timestamp":1760228731178,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,5,23]],"date-time":"2022-05-23T00:00:00Z","timestamp":1653264000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"High-Potential Individuals Global Training Program","award":["2021-0-01553","NRF-2020R1A2C4001623"],"award-info":[{"award-number":["2021-0-01553","NRF-2020R1A2C4001623"]}]},{"name":"the National Research Foundation of Korea (NRF) grant","award":["2021-0-01553","NRF-2020R1A2C4001623"],"award-info":[{"award-number":["2021-0-01553","NRF-2020R1A2C4001623"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>MRI is an imaging technology that non-invasively obtains high-quality medical images for diagnosis. However, MRI has the major disadvantage of long scan times which cause patient discomfort and image artifacts. As one of the methods for reducing the long scan time of MRI, the parallel MRI method for reconstructing a high-fidelity MR image from under-sampled multi-coil k-space data is widely used. In this study, we propose a method to reconstruct a high-fidelity MR image from under-sampled multi-coil k-space data using deep-learning. The proposed multi-domain Neumann network with sensitivity maps (MDNNSM) is based on the Neumann network and uses a forward model including coil sensitivity maps for parallel MRI reconstruction. The MDNNSM consists of three main structures: the CNN-based sensitivity reconstruction block estimates coil sensitivity maps from multi-coil under-sampled k-space data; the recursive MR image reconstruction block reconstructs the MR image; and the skip connection accumulates each output and produces the final result. Experiments using the fastMRI T1-weighted brain image dataset were conducted at acceleration factors of 2, 4, and 8. Qualitative and quantitative experimental results show that the proposed MDNNSM method reconstructs MR images more accurately than other methods, including the generalized autocalibrating partially parallel acquisitions (GRAPPA) method and the original Neumann network.<\/jats:p>","DOI":"10.3390\/s22103943","type":"journal-article","created":{"date-parts":[[2022,5,25]],"date-time":"2022-05-25T00:14:14Z","timestamp":1653437654000},"page":"3943","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Multi-Domain Neumann Network with Sensitivity Maps for Parallel MRI Reconstruction"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7489-5829","authenticated-orcid":false,"given":"Jun-Hyeok","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Biomedical Engineering, Hankuk University of Foreign Studies, Yongin 17035, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junghwa","family":"Kang","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, Hankuk University of Foreign Studies, Yongin 17035, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Se-Hong","family":"Oh","sequence":"additional","affiliation":[{"name":"Department of Biomedical Engineering, Hankuk University of Foreign Studies, Yongin 17035, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9186-4095","authenticated-orcid":false,"given":"Dong Hye","family":"Ye","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Marquette University, Milwaukee, WI 53323, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1002\/jmri.10451","article-title":"K-space in the clinic","volume":"19","author":"Paschal","year":"2004","journal-title":"J. Magn. Reson. Imaging"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1007\/s00330-003-1992-7","article-title":"A brief review of parallel magnetic resonance imaging","volume":"13","author":"Heidemann","year":"2003","journal-title":"Eur. Radiol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"952","DOI":"10.1002\/(SICI)1522-2594(199911)42:5<952::AID-MRM16>3.0.CO;2-S","article-title":"SENSE: Sensitivity encoding for fast MRI","volume":"42","author":"Pruessmann","year":"1999","journal-title":"Magn. Reson. Med."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1196","DOI":"10.1002\/mrm.21245","article-title":"Joint image reconstruction and sensitivity estimation in SENSE (JSENSE)","volume":"57","author":"Ying","year":"2007","journal-title":"Magn. Reson. Med."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1002\/mrm.10171","article-title":"Generalized autocalibrating partially parallel acquisitions (GRAPPA)","volume":"47","author":"Griswold","year":"2002","journal-title":"Magn. Reson. Med."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1002\/mrm.22428","article-title":"SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space","volume":"64","author":"Lustig","year":"2010","journal-title":"Magn. Reson. Med."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"990","DOI":"10.1002\/mrm.24751","article-title":"ESPIRiT\u2014An eigenvalue approach to autocalibrating parallel MRI: Where SENSE meets GRAPPA","volume":"71","author":"Uecker","year":"2014","journal-title":"Magn. Reson. Med."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3142","DOI":"10.1109\/TIP.2017.2662206","article-title":"Beyond a gaussian denoiser: Residual learning of deep cnn for image denoising","volume":"26","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Image Process."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zhang, K., Zuo, W., Gu, S., and Zhang, L. (2017, January 21\u201326). Learning deep CNN denoiser prior for image restoration. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.300"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.neunet.2019.12.024","article-title":"Attention-guided CNN for image denoising","volume":"124","author":"Tian","year":"2020","journal-title":"Neural Netw."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1109\/TPAMI.2015.2439281","article-title":"Image super-resolution using deep convolutional networks","volume":"38","author":"Dong","year":"2015","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Lai, W.S., Huang, J.B., Ahuja, N., and Yang, M.H. (2017, January 21\u201326). Deep laplacian pyramid networks for fast and accurate super-resolution. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.618"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Yamanaka, J., Kuwashima, S., and Kurita, T. (2017, January 14\u201318). Fast and accurate image super resolution by deep CNN with skip connection and network in network. Proceedings of the International Conference on Neural Information Processing, Guangzhou, China.","DOI":"10.1007\/978-3-319-70096-0_23"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Li, K., Li, K., Wang, L., Zhong, B., and Fu, Y. (2018, January 8\u201314). Image super-resolution using very deep residual channel attention networks. Proceedings of the European Conference on Computer Vision (ECCV), Munich, Germany.","DOI":"10.1007\/978-3-030-01234-2_18"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Yan, Z., Li, X., Li, M., Zuo, W., and Shan, S. (2018, January 8\u201314). Shift-net: Image inpainting via deep feature rearrangement. Proceedings of the European Conference on Computer Vision (ECCV), Munich, Germany.","DOI":"10.1007\/978-3-030-01264-9_1"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Zeng, Y., Fu, J., Chao, H., and Guo, B. (2019, January 15\u201320). Learning pyramid-context encoder network for high-quality image inpainting. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00158"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Pathak, D., Krahenbuhl, P., Donahue, J., Darrell, T., and Efros, A.A. (2016, January 27\u201330). Context encoders: Feature learning by inpainting. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.278"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1109\/TMI.2018.2865356","article-title":"MoDL: Model-based deep learning architecture for inverse problems","volume":"38","author":"Aggarwal","year":"2018","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1109\/TCI.2019.2948732","article-title":"Neumann networks for linear inverse problems in imaging","volume":"6","author":"Gilton","year":"2019","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_20","unstructured":"Diamond, S., Sitzmann, V., Heide, F., and Wetzstein, G. (2017). Unrolled optimization with deep priors. arXiv."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1109\/TMI.2017.2760978","article-title":"A deep cascade of convolutional neural networks for dynamic MR image reconstruction","volume":"37","author":"Schlemper","year":"2017","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"101689","DOI":"10.1016\/j.media.2020.101689","article-title":"Accelerating Cartesian MRI by domain-transform manifold learning in phase-encoding direction","volume":"63","author":"Eo","year":"2020","journal-title":"Med. Image Anal."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wang, S., Su, Z., Ying, L., Peng, X., Zhu, S., Liang, F., Feng, D., and Liang, D. (2016, January 13\u201316). Accelerating magnetic resonance imaging via deep learning. Proceedings of the 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI), Prague, Czech Republic.","DOI":"10.1109\/ISBI.2016.7493320"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"102098","DOI":"10.1016\/j.media.2021.102098","article-title":"Adaptive convolutional neural networks for accelerating magnetic resonance imaging via k-space data interpolation","volume":"72","author":"Du","year":"2021","journal-title":"Med. Image Anal."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1985","DOI":"10.1109\/TBME.2018.2821699","article-title":"Deep residual learning for accelerated MRI using magnitude and phase networks","volume":"65","author":"Lee","year":"2018","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_26","unstructured":"Tavaf, N., Torfi, A., Ugurbil, K., and Van de Moortele, P.F. (2021). GRAPPA-GANs for Parallel MRI Reconstruction. arXiv."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2188","DOI":"10.1002\/mrm.27201","article-title":"KIKI-net: Cross-domain convolutional neural networks for reconstructing undersampled magnetic resonance images","volume":"80","author":"Eo","year":"2018","journal-title":"Magn. Reson. Med."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1109\/TMI.2019.2927101","article-title":"k-space deep learning for accelerated MRI","volume":"39","author":"Han","year":"2019","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Sriram, A., Zbontar, J., Murrell, T., Zitnick, C.L., Defazio, A., and Sodickson, D.K. (2020, January 13\u201319). GrappaNet: Combining parallel imaging with deep learning for multi-coil MRI reconstruction. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.01432"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3055","DOI":"10.1002\/mrm.26977","article-title":"Learning a variational network for reconstruction of accelerated MRI data","volume":"79","author":"Hammernik","year":"2018","journal-title":"Magn. Reson. Med."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Sriram, A., Zbontar, J., Murrell, T., Defazio, A., Zitnick, C.L., Yakubova, N., Knoll, F., and Johnson, P. (2020, January 4\u20138). End-to-end variational networks for accelerated MRI reconstruction. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Lima, Peru.","DOI":"10.1007\/978-3-030-59713-9_7"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Jun, Y., Shin, H., Eo, T., and Hwang, D. (2021, January 20\u201325). Joint deep model-based MR image and coil sensitivity reconstruction network (joint-ICNet) for fast MRI. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Nashville, TN, USA.","DOI":"10.1109\/CVPR46437.2021.00523"},{"key":"ref_33","unstructured":"Putzky, P., Karkalousos, D., Teuwen, J., Miriakov, N., Bakker, B., Caan, M., and Welling, M. (2019). i-RIM applied to the fastMRI challenge. arXiv."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1086","DOI":"10.1002\/mrm.21236","article-title":"Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint","volume":"57","author":"Block","year":"2007","journal-title":"Magn. Reson. Med."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1002\/mrm.22595","article-title":"Second order total generalized variation (TGV) for MRI","volume":"65","author":"Knoll","year":"2011","journal-title":"Magn. Reson. Med."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","article-title":"Compressed sensing","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1109\/MSP.2007.914728","article-title":"Compressed sensing MRI","volume":"25","author":"Lustig","year":"2008","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016, January 27\u201330). Deep residual learning for image recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Ronneberger, O., Fischer, P., and Brox, T. (2015, January 5\u20139). U-net: Convolutional networks for biomedical image segmentation. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Munich, Germany.","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"ref_40","unstructured":"Ulyanov, D., Vedaldi, A., and Lempitsky, V. (2016). Instance normalization: The missing ingredient for fast stylization. arXiv."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_42","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_43","unstructured":"Zbontar, J., Knoll, F., Sriram, A., Murrell, T., Huang, Z., Muckley, M.J., Defazio, A., Stern, R., Johnson, P., and Bruno, M. (2018). fastMRI: An open dataset and benchmarks for accelerated MRI. arXiv."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"e190007","DOI":"10.1148\/ryai.2020190007","article-title":"fastMRI: A publicly available raw k-space and DICOM dataset of knee images for accelerated MR image reconstruction using machine learning","volume":"2","author":"Knoll","year":"2020","journal-title":"Radiol. Artif. Intell."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/10\/3943\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:16:52Z","timestamp":1760138212000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/10\/3943"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,23]]},"references-count":44,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["s22103943"],"URL":"https:\/\/doi.org\/10.3390\/s22103943","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,5,23]]}}}