{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T07:42:20Z","timestamp":1763624540368,"version":"3.45.0"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T00:00:00Z","timestamp":1750809600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T00:00:00Z","timestamp":1750809600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"the Science and Technology Research Program of Chongqing Municipal Education Commission","award":["KJQN202301303","KJZDK202303103"],"award-info":[{"award-number":["KJQN202301303","KJZDK202303103"]}]},{"DOI":"10.13039\/501100002867","name":"Foundation of Chongqing University of Arts and Sciences","doi-asserted-by":"crossref","award":["R2022DQ04"],"award-info":[{"award-number":["R2022DQ04"]}],"id":[{"id":"10.13039\/501100002867","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Med Biol Eng Comput"],"published-print":{"date-parts":[[2025,11]]},"DOI":"10.1007\/s11517-025-03399-7","type":"journal-article","created":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T03:43:47Z","timestamp":1750823027000},"page":"3335-3355","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["3D Magnetic resonance image denoising using nonlocal and nonconvex tensor train regularization"],"prefix":"10.1007","volume":"63","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9731-437X","authenticated-orcid":false,"given":"Li","family":"Wang","sequence":"first","affiliation":[]},{"given":"Yun","family":"Zhao","sequence":"additional","affiliation":[]},{"given":"Liang","family":"Zhao","sequence":"additional","affiliation":[]},{"given":"Bin","family":"Jiang","sequence":"additional","affiliation":[]},{"given":"Qinling","family":"Xia","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,6,25]]},"reference":[{"issue":"7","key":"3399_CR1","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1109\/34.56205","volume":"12","author":"P Perona","year":"1990","unstructured":"Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629\u2013639","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"1\u20134","key":"3399_CR2","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0167-2789(92)90242-F","volume":"60","author":"LI Rudin","year":"1992","unstructured":"Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D 60(1\u20134):259\u2013268","journal-title":"Physica D"},{"issue":"10","key":"3399_CR3","doi-asserted-by":"publisher","first-page":"2265","DOI":"10.1109\/TIP.2009.2025553","volume":"18","author":"K Krissian","year":"2009","unstructured":"Krissian K, Aja-Fern\u00e1ndez S (2009) Noise-driven anisotropic diffusion filtering of MRI. IEEE Trans Image Process 18(10):2265\u20132274","journal-title":"IEEE Trans Image Process"},{"issue":"4","key":"3399_CR4","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1109\/TCBB.2014.2344675","volume":"12","author":"HM Golshan","year":"2014","unstructured":"Golshan HM, Hasanzadeh RP (2014) An optimized LMMSE based method for 3D MRI denoising. IEEE\/ACM Trans Comput Biol Bioinf 12(4):861\u2013870","journal-title":"IEEE\/ACM Trans Comput Biol Bioinf"},{"key":"3399_CR5","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/j.bspc.2015.04.015","volume":"20","author":"P Sudeep","year":"2015","unstructured":"Sudeep P, Palanisamy P, Kesavadas C, Rajan J (2015) Nonlocal linear minimum mean square error methods for denoising MRI. Biomed Signal Process Control 20:125\u2013134","journal-title":"Biomed Signal Process Control"},{"key":"3399_CR6","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/j.patrec.2018.02.007","volume":"139","author":"P Sudeep","year":"2020","unstructured":"Sudeep P, Palanisamy P, Kesavadas C, Rajan J (2020) An improved nonlocal maximum likelihood estimation method for denoising magnetic resonance images with spatially varying noise levels. Pattern Recogn Lett 139:34\u201341","journal-title":"Pattern Recogn Lett"},{"issue":"6","key":"3399_CR7","doi-asserted-by":"publisher","first-page":"842","DOI":"10.1016\/j.mri.2010.03.013","volume":"28","author":"CS Anand","year":"2010","unstructured":"Anand CS, Sahambi JS (2010) Wavelet domain non-linear filtering for MRI denoising. Magn Reson Imaging 28(6):842\u2013861","journal-title":"Magn Reson Imaging"},{"key":"3399_CR8","doi-asserted-by":"crossref","unstructured":"Biswas R, Purkayastha D, Roy S (2018) Denoising of MRI images using curvelet transform.\u00a0Advances in Systems, Control and Automation: ETAEERE-2016, pp. 575\u2013583","DOI":"10.1007\/978-981-10-4762-6_55"},{"key":"3399_CR9","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/s40009-016-0498-1","volume":"40","author":"S Anila","year":"2017","unstructured":"Anila S, Sivaraju S, Devarajan N (2017) A new contourlet based multiresolution approximation for MRI image noise removal. National Academy Science Letters 40:39\u201341","journal-title":"National Academy Science Letters"},{"key":"3399_CR10","doi-asserted-by":"crossref","unstructured":"Buades A, Coll B, Morel J.-M. (2005) A non-local algorithm for image denoising. In 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05)\u00a02:60\u201365","DOI":"10.1109\/CVPR.2005.38"},{"key":"3399_CR11","doi-asserted-by":"crossref","unstructured":"Hanchate V, Joshi K (2020) Denoising of MRI images using fast NLM.\u00a0Indones J Electr Eng Comput Sci\u00a018(1):135\u2013141","DOI":"10.11591\/ijeecs.v18.i1.pp135-141"},{"key":"3399_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s12880-019-0407-4","volume":"20","author":"K Chen","year":"2020","unstructured":"Chen K, Lin X, Hu X, Wang J, Zhong H, Jiang L (2020) An enhanced adaptive non-local means algorithm for Rician noise reduction in magnetic resonance brain images. BMC Med Imaging 20:1\u20139","journal-title":"BMC Med Imaging"},{"key":"3399_CR13","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/j.bspc.2016.05.007","volume":"30","author":"C Singh","year":"2016","unstructured":"Singh C, Ranade SK, Singh K (2016) Invariant moments and transform-based unbiased nonlocal means for denoising of MR images. Biomed Signal Process Control 30:13\u201324","journal-title":"Biomed Signal Process Control"},{"issue":"6","key":"3399_CR14","doi-asserted-by":"publisher","first-page":"1331","DOI":"10.1007\/s11760-021-01864-y","volume":"15","author":"A Sharma","year":"2021","unstructured":"Sharma A, Chaurasia V (2021) MRI denoising using advanced NLM filtering with non-subsampled shearlet transform. SIViP 15(6):1331\u20131339","journal-title":"SIViP"},{"key":"3399_CR15","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1016\/j.bspc.2018.08.031","volume":"47","author":"HV Bhujle","year":"2019","unstructured":"Bhujle HV, Vadavadagi BH (2019) NLM based magnetic resonance image denoising\u2013a review. Biomed Signal Process Control 47:252\u2013261","journal-title":"Biomed Signal Process Control"},{"issue":"4","key":"3399_CR16","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1016\/j.media.2008.02.004","volume":"12","author":"JV Manj\u00f3n","year":"2008","unstructured":"Manj\u00f3n JV, Carbonell-Caballero J, Lull JJ, Garc\u00eda-Mart\u00ed G, Mart\u00ed-Bonmat\u00ed L, Robles M (2008) MRI denoising using non-local means. Med Image Anal 12(4):514\u2013523","journal-title":"Med Image Anal"},{"issue":"8","key":"3399_CR17","doi-asserted-by":"publisher","first-page":"2080","DOI":"10.1109\/TIP.2007.901238","volume":"16","author":"K Dabov","year":"2007","unstructured":"Dabov K, Foi A, Katkovnik V, Egiazarian K (2007) Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans Image Process 16(8):2080\u20132095","journal-title":"IEEE Trans Image Process"},{"issue":"1","key":"3399_CR18","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1109\/TIP.2012.2210725","volume":"22","author":"M Maggioni","year":"2012","unstructured":"Maggioni M, Katkovnik V, Egiazarian K, Foi A (2012) Nonlocal transform-domain filter for volumetric data denoising and reconstruction. IEEE Trans Image Process 22(1):119\u2013133","journal-title":"IEEE Trans Image Process"},{"issue":"1","key":"3399_CR19","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.media.2011.04.003","volume":"16","author":"JV Manj\u00f3n","year":"2012","unstructured":"Manj\u00f3n JV, Coup\u00e9 P, Buades A, Collins DL, Robles M (2012) New methods for MRI denoising based on sparseness and self-similarity. Med Image Anal 16(1):18\u201327","journal-title":"Med Image Anal"},{"key":"3399_CR20","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/j.bspc.2017.01.016","volume":"34","author":"Y Xia","year":"2017","unstructured":"Xia Y, Gao Q, Cheng N, Lu Y, Zhang D, Ye Q (2017) Denoising 3-D magnitude magnetic resonance images based on weighted nuclear norm minimization. Biomed Signal Process Control 34:183\u2013194","journal-title":"Biomed Signal Process Control"},{"key":"3399_CR21","doi-asserted-by":"crossref","unstructured":"Chen Z, Zhou Z, Adnan S (2021) Joint low-rank prior and difference of Gaussian filter for magnetic resonance image denoising.\u00a0Medical & Biological Engineering & Computing, no. 1","DOI":"10.1007\/s11517-020-02312-8"},{"key":"3399_CR22","doi-asserted-by":"publisher","first-page":"45858","DOI":"10.1109\/ACCESS.2019.2907637","volume":"7","author":"Y Zhang","year":"2019","unstructured":"Zhang Y, Yang Z, Hu J, Zou S, Fu Y (2019) MRI denoising using low rank prior and sparse gradient prior. IEEE Access 7:45858\u201345865","journal-title":"IEEE Access"},{"key":"3399_CR23","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/j.brainresbull.2018.08.006","volume":"142","author":"L Zhai","year":"2018","unstructured":"Zhai L, Fu S, Lv H, Zhang C, Wang F (2018) Weighted Schatten p-norm minimization for 3D magnetic resonance images denoising. Brain Res Bull 142:270\u2013280","journal-title":"Brain Res Bull"},{"key":"3399_CR24","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1109\/RBME.2021.3055556","volume":"15","author":"PK Mishro","year":"2021","unstructured":"Mishro PK, Agrawal S, Panda R, Abraham A (2021) A survey on state-of-the-art denoising techniques for brain magnetic resonance images. IEEE Rev Biomed Eng 15:184\u2013199","journal-title":"IEEE Rev Biomed Eng"},{"key":"3399_CR25","volume":"465","author":"C Pan","year":"2024","unstructured":"Pan C, Ling C, He H, Qi L, Xu Y (2024) A low-rank and sparse enhanced Tucker decomposition approach for tensor completion. Appl Math Comput 465","journal-title":"Appl Math Comput"},{"key":"3399_CR26","unstructured":"Qiu Y, Zhou G, Zhao Q, Xie S (2022) Noisy tensor completion via low-rank tensor ring. IEEE Transactions on Neural Networks and Learning Systems"},{"key":"3399_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/LGRS.2023.3329687","volume":"20","author":"Q Zhang","year":"2023","unstructured":"Zhang Q, Dong Y, Yuan Q, Song M, Yu H (2023) Combined deep priors with low-rank tensor factorization for hyperspectral image restoration. IEEE Geosci Remote Sens Lett 20:1\u20135","journal-title":"IEEE Geosci Remote Sens Lett"},{"issue":"4","key":"3399_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/s11432-022-3609-4","volume":"66","author":"N Liu","year":"2023","unstructured":"Liu N, Li W, Wang Y, Tao R, Du Q, Chanussot J (2023) A survey on hyperspectral image restoration: from the view of low-rank tensor approximation. SCIENCE CHINA Inf Sci 66(4)","journal-title":"SCIENCE CHINA Inf Sci"},{"key":"3399_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/LGRS.2023.3251861","volume":"20","author":"MM Salut","year":"2023","unstructured":"Salut MM, Anderson DV (2023) Randomized tensor robust PCA for noisy hyperspectral image classification. IEEE Geosci Remote Sens Lett 20:1\u20135","journal-title":"IEEE Geosci Remote Sens Lett"},{"key":"3399_CR30","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.sigpro.2018.10.018","volume":"156","author":"P Jing","year":"2019","unstructured":"Jing P, Su Y, Li Z, Liu J, Nie L (2019) Low-rank regularized tensor discriminant representation for image set classification. Signal Process 156:62\u201370","journal-title":"Signal Process"},{"key":"3399_CR31","doi-asserted-by":"publisher","first-page":"28684","DOI":"10.1109\/ACCESS.2021.3058103","volume":"9","author":"S Ahmadi-Asl","year":"2021","unstructured":"Ahmadi-Asl S et al (2021) Randomized algorithms for computation of Tucker decomposition and higher order SVD (HOSVD). IEEE Access 9:28684\u201328706","journal-title":"IEEE Access"},{"key":"3399_CR32","doi-asserted-by":"crossref","unstructured":"Zhang Z, Ely G, Aeron S, Hao N, Kilmer M (2014) Novel methods for multilinear data completion and de-noising based on tensor-SVD. In Proceedings of the IEEE conference on computer vision and pattern recognition\u00a0pp. 3842\u20133849","DOI":"10.1109\/CVPR.2014.485"},{"key":"3399_CR33","doi-asserted-by":"publisher","DOI":"10.1016\/j.bspc.2021.103302","volume":"72","author":"L Wang","year":"2022","unstructured":"Wang L, Xiao D, Hou WS, Wu XY, Jiang B, Chen L (2022) A nonlocal enhanced Low-Rank tensor approximation framework for 3D Magnetic Resonance image denoising. Biomed Signal Process Control 72","journal-title":"Biomed Signal Process Control"},{"issue":"1","key":"3399_CR34","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/j.media.2014.08.004","volume":"19","author":"X Zhang","year":"2015","unstructured":"Zhang X et al (2015) Denoising of 3D magnetic resonance images by using higher-order singular value decomposition. Med Image Anal 19(1):75\u201386","journal-title":"Med Image Anal"},{"issue":"4","key":"3399_CR35","doi-asserted-by":"publisher","first-page":"941","DOI":"10.1109\/TMI.2017.2778230","volume":"37","author":"Z Kong","year":"2017","unstructured":"Kong Z, Han L, Liu X, Yang X (2017) A new 4-D nonlocal transform-domain filter for 3-D magnetic resonance images denoising. IEEE Trans Med Imaging 37(4):941\u2013954","journal-title":"IEEE Trans Med Imaging"},{"key":"3399_CR36","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.bspc.2018.04.004","volume":"44","author":"HS Khaleel","year":"2018","unstructured":"Khaleel HS, Sagheer SVM, Baburaj M, George SN (2018) Denoising of Rician corrupted 3D magnetic resonance images using tensor-SVD. Biomed Signal Process Control 44:82\u201395","journal-title":"Biomed Signal Process Control"},{"key":"3399_CR37","volume":"367","author":"J-H Yang","year":"2020","unstructured":"Yang J-H, Zhao X-L, Ji T-Y, Ma T-H, Huang T-Z (2020) Low-rank tensor train for tensor robust principal component analysis. Appl Math Comput 367","journal-title":"Appl Math Comput"},{"issue":"10","key":"3399_CR38","doi-asserted-by":"publisher","first-page":"4842","DOI":"10.1109\/TIP.2016.2599290","volume":"25","author":"Y Xie","year":"2016","unstructured":"Xie Y, Gu S, Liu Y, Zuo W, Zhang W, Zhang L (2016) Weighted Schatten p-norm minimization for image denoising and background subtraction. IEEE Trans Image Process 25(10):4842\u20134857","journal-title":"IEEE Trans Image Process"},{"key":"3399_CR39","doi-asserted-by":"crossref","unstructured":"Zuo W, Meng D, Zhang L, Feng X, Zhang D (2013) A generalized iterated shrinkage algorithm for non-convex sparse coding. In Proceedings of the IEEE international conference on computer vision, pp. 217\u2013224","DOI":"10.1109\/ICCV.2013.34"},{"issue":"1","key":"3399_CR40","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1002\/jmri.22003","volume":"31","author":"JV Manj\u00f3n","year":"2010","unstructured":"Manj\u00f3n JV, Coup\u00e9 P, Mart\u00ed-Bonmat\u00ed L, Collins DL, Robles M (2010) Adaptive non-local means denoising of MR images with spatially varying noise levels. J Magn Reson Imaging 31(1):192\u2013203","journal-title":"J Magn Reson Imaging"},{"issue":"9","key":"3399_CR41","doi-asserted-by":"publisher","first-page":"1498","DOI":"10.1162\/jocn.2007.19.9.1498","volume":"19","author":"DS Marcus","year":"2007","unstructured":"Marcus DS, Wang TH, Parker J, Csernansky JG, Morris JC, Buckner RL (2007) Open Access Series of Imaging Studies (OASIS): cross-sectional MRI data in young, middle aged, nondemented, and demented older adults. J Cogn Neurosci 19(9):1498\u20131507","journal-title":"J Cogn Neurosci"},{"key":"3399_CR42","doi-asserted-by":"crossref","unstructured":"Foi A (2011) Noise estimation and removal in MR imaging: the variance-stabilization approach. In 2011 IEEE International symposium on biomedical imaging: from nano to macro, pp. 1809\u20131814","DOI":"10.1109\/ISBI.2011.5872758"},{"issue":"12","key":"3399_CR43","doi-asserted-by":"publisher","first-page":"3116","DOI":"10.1109\/TIP.2010.2052820","volume":"19","author":"X Zhu","year":"2010","unstructured":"Zhu X, Milanfar P (2010) Automatic parameter selection for denoising algorithms using a no-reference measure of image content. IEEE Trans Image Process 19(12):3116\u20133132","journal-title":"IEEE Trans Image Process"},{"key":"3399_CR44","unstructured":"Li Wang A lecturer in Chongqing University of Arts and Sciences, mainly engaged in the research of medical image processing"}],"container-title":["Medical &amp; Biological Engineering &amp; Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11517-025-03399-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11517-025-03399-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11517-025-03399-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T07:33:24Z","timestamp":1763624004000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11517-025-03399-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,25]]},"references-count":44,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["3399"],"URL":"https:\/\/doi.org\/10.1007\/s11517-025-03399-7","relation":{},"ISSN":["0140-0118","1741-0444"],"issn-type":[{"type":"print","value":"0140-0118"},{"type":"electronic","value":"1741-0444"}],"subject":[],"published":{"date-parts":[[2025,6,25]]},"assertion":[{"value":"24 November 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 June 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}