{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T02:29:19Z","timestamp":1786415359930,"version":"build-2736575974"},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T00:00:00Z","timestamp":1785283200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T00:00:00Z","timestamp":1785283200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12501020"],"award-info":[{"award-number":["12501020"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006469","name":"Macao Science and Technology Development Fund","doi-asserted-by":"crossref","award":["No. 0013\/2021\/ITP"],"award-info":[{"award-number":["No. 0013\/2021\/ITP"]}],"id":[{"id":"10.13039\/501100006469","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100006469","name":"Macao Science and Technology Development Fund","doi-asserted-by":"crossref","award":["12371023, 12271338"],"award-info":[{"award-number":["12371023, 12271338"]}],"id":[{"id":"10.13039\/501100006469","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"crossref","award":["RGPIN 2020-06746"],"award-info":[{"award-number":["RGPIN 2020-06746"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2026,9]]},"DOI":"10.1007\/s10915-026-03279-8","type":"journal-article","created":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T10:38:19Z","timestamp":1785321499000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Efficient Quaternion Tensor Completion via $$L_{2,1}$$-Norm and QR Decomposition"],"prefix":"10.1007","volume":"108","author":[{"given":"Jian","family":"Sun","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9646-4448","authenticated-orcid":false,"given":"Xin","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liang","family":"Xiao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui","family":"Luo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,29]]},"reference":[{"issue":"4","key":"3279_CR1","doi-asserted-by":"publisher","first-page":"308","DOI":"10.26599\/BDMA.2018.9020008","volume":"1","author":"A Ramlatchan","year":"2018","unstructured":"Ramlatchan, A., Yang, M., Liu, Q., Li, M., Wang, J., Li, Y.: A survey of matrix completion methods for recommendation systems. Big Data Mining and Analytics 1(4), 308\u2013323 (2018)","journal-title":"Big Data Mining and Analytics"},{"issue":"8","key":"3279_CR2","first-page":"1261","volume":"25","author":"F Cao","year":"2014","unstructured":"Cao, F., Cai, M., Tan, Y.: Image interpolation via low-rank matrix completion and recovery. IEEE Trans. Circuits Syst. Video Technol. 25(8), 1261\u20131270 (2014)","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"3279_CR3","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1109\/TIP.2021.3128321","volume":"31","author":"J Miao","year":"2021","unstructured":"Miao, J., Kou, K.I.: Color image recovery using low-rank quaternion matrix completion algorithm. IEEE Trans. Image Process. 31, 190\u2013201 (2021)","journal-title":"IEEE Trans. Image Process."},{"key":"3279_CR4","doi-asserted-by":"publisher","first-page":"7801","DOI":"10.1109\/TIP.2025.3633566","volume":"34","author":"H Zeng","year":"2025","unstructured":"Zeng, H., Li, W., Peng, X., Xiao, M.: Multidimensional Imaging Data Completion via Weighted Three-Directional Minimax Concave Penalty Regularization. IEEE Trans. Image Process. 34, 7801\u20137816 (2025)","journal-title":"IEEE Trans. Image Process."},{"issue":"6","key":"3279_CR5","doi-asserted-by":"publisher","first-page":"3011","DOI":"10.1109\/TIP.2018.2812100","volume":"27","author":"G Xia","year":"2018","unstructured":"Xia, G., Sun, H., Chen, B., Liu, Q., Feng, L., Zhang, G., Hang, R.: Nonlinear low-rank matrix completion for human motion recovery. IEEE Trans. Image Process. 27(6), 3011\u20133024 (2018)","journal-title":"IEEE Trans. Image Process."},{"key":"3279_CR6","doi-asserted-by":"crossref","unstructured":"Bac, S., Quiton, S.J., Kron, K.J., Chae, J., Mitra, U., Mallikarjun Sharada, S.: A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions. J. Chem. Phys. 156(18), (2022)","DOI":"10.1063\/5.0091155"},{"issue":"1","key":"3279_CR7","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1109\/TPAMI.2012.39","volume":"35","author":"J Liu","year":"2012","unstructured":"Liu, J., Musialski, P., Wonka, P., Ye, J.: Tensor completion for estimating missing values in visual data. IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 208\u2013220 (2012)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"3","key":"3279_CR8","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2299","volume":"27","author":"G Song","year":"2020","unstructured":"Song, G., Ng, M.K., Zhang, X.: Robust tensor completion using transformed tensor singular value decomposition. Numerical Linear Algebra with Applications 27(3), e2299 (2020)","journal-title":"Numerical Linear Algebra with Applications"},{"issue":"7","key":"3279_CR9","doi-asserted-by":"publisher","first-page":"1411","DOI":"10.3390\/app9071411","volume":"9","author":"S Cai","year":"2019","unstructured":"Cai, S., Luo, Q., Yang, M., Li, W., Xiao, M.: Tensor robust principal component analysis via non-convex low rank approximation. Appl. Sci. 9(7), 1411 (2019)","journal-title":"Appl. Sci."},{"issue":"5","key":"3279_CR10","doi-asserted-by":"publisher","first-page":"605","DOI":"10.1016\/j.patrec.2011.11.015","volume":"33","author":"TD Nguyen","year":"2012","unstructured":"Nguyen, T.D., Lee, G.: Color image segmentation using tensor voting based color clustering. Pattern Recogn. Lett. 33(5), 605\u2013614 (2012)","journal-title":"Pattern Recogn. Lett."},{"key":"3279_CR11","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1016\/j.ins.2023.02.012","volume":"629","author":"F Wu","year":"2023","unstructured":"Wu, F., Li, C., Li, Y.: Robust low-rank tensor completion via new regularized model with approximate SVD. Inf. Sci. 629, 646\u2013666 (2023)","journal-title":"Inf. Sci."},{"issue":"6","key":"3279_CR12","doi-asserted-by":"publisher","first-page":"3367","DOI":"10.1109\/TGRS.2017.2670021","volume":"55","author":"MKP Ng","year":"2017","unstructured":"Ng, M.K.P., Yuan, Q., Yan, L., Sun, J.: An adaptive weighted tensor completion method for the recovery of remote sensing images with missing data. IEEE Trans. Geosci. Remote Sens. 55(6), 3367\u20133381 (2017)","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"3279_CR13","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1016\/j.cam.2019.06.004","volume":"363","author":"JH Yang","year":"2020","unstructured":"Yang, J.H., Zhao, X.L., Ma, T.H., Chen, Y., Huang, T.Z., Ding, M.: Remote sensing images destriping using unidirectional hybrid total variation and nonconvex low-rank regularization. J. Comput. Appl. Math. 363, 124\u2013144 (2020)","journal-title":"J. Comput. Appl. Math."},{"issue":"6","key":"3279_CR14","doi-asserted-by":"publisher","first-page":"1511","DOI":"10.1109\/TSP.2016.2639466","volume":"65","author":"Z Zhang","year":"2016","unstructured":"Zhang, Z., Aeron, S.: Exact tensor completion using t-SVD. IEEE Trans. Signal Process. 65(6), 1511\u20131526 (2016)","journal-title":"IEEE Trans. Signal Process."},{"issue":"20","key":"3279_CR15","doi-asserted-by":"publisher","first-page":"5423","DOI":"10.1109\/TSP.2016.2586759","volume":"64","author":"T Yokota","year":"2016","unstructured":"Yokota, T., Zhao, Q., Cichocki, A.: Smooth PARAFAC decomposition for tensor completion. IEEE Trans. Signal Process. 64(20), 5423\u20135436 (2016)","journal-title":"IEEE Trans. Signal Process."},{"issue":"3","key":"3279_CR16","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/s10915-021-01679-6","volume":"89","author":"M Li","year":"2021","unstructured":"Li, M., Li, W., Chen, Y., Xiao, M.: The nonconvex tensor robust principal component analysis approximation model via the weighted $$L_{p}$$-norm regularization. J. Sci. Comput. 89(3), 67 (2021)","journal-title":"J. Sci. Comput."},{"key":"3279_CR17","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Ely, G., Aeron, S., Hao, N., Kilmer, M.: \u201cNovel methods for multilinear data completion and de-noising based on tensor-SVD,\u201d in Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 3842\u20133849, (2014)","DOI":"10.1109\/CVPR.2014.485"},{"key":"3279_CR18","doi-asserted-by":"crossref","unstructured":"Xue, S., Qiu, W., Liu, F., Jin, X.: Low-rank tensor completion by truncated nuclear norm regularization, in 2018 24th International Conference on Pattern Recognition (ICPR). IEEE, pp. 2600\u20132605, (2018)","DOI":"10.1109\/ICPR.2018.8546008"},{"key":"3279_CR19","doi-asserted-by":"publisher","first-page":"1267","DOI":"10.1109\/TCI.2021.3130977","volume":"7","author":"F Wu","year":"2021","unstructured":"Wu, F., Li, Y., Li, C., Wu, Y.: A fast tensor completion method based on tensor QR decomposition and tensor nuclear norm minimization. IEEE Transactions on Computational Imaging 7, 1267\u20131277 (2021)","journal-title":"IEEE Transactions on Computational Imaging"},{"issue":"3","key":"3279_CR20","doi-asserted-by":"publisher","first-page":"803","DOI":"10.1109\/TNNLS.2018.2851957","volume":"30","author":"Q Liu","year":"2018","unstructured":"Liu, Q., Davoine, F., Yang, J., Cui, Y., Jin, Z., Han, F.: A fast and accurate matrix completion method based on QR decomposition and $$ L_ 2, 1 $$-norm minimization. IEEE Transactions on Neural Networks and Learning Systems 30(3), 803\u2013817 (2018)","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"3279_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2021.108240","volume":"189","author":"Y Zheng","year":"2021","unstructured":"Zheng, Y., Xu, A.B.: Tensor completion via tensor QR decomposition and $$ L_ 2, 1 $$-norm minimization. Signal Process. 189, 108240 (2021)","journal-title":"Signal Process."},{"key":"3279_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2021.108088","volume":"185","author":"Y Chen","year":"2021","unstructured":"Chen, Y., Jia, Z.G., Peng, Y., Peng, Y.X., Zhang, D.: A new structure-preserving quaternion qr decomposition method for color image blind watermarking. Signal Process. 185, 108088 (2021)","journal-title":"Signal Process."},{"key":"3279_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2020.107505","volume":"107","author":"J Miao","year":"2020","unstructured":"Miao, J., Kou, K.I., Liu, W.: Low-rank quaternion tensor completion for recovering color videos and images. Pattern Recogn. 107, 107505 (2020)","journal-title":"Pattern Recogn."},{"issue":"4","key":"3279_CR24","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2245","volume":"26","author":"Z Jia","year":"2019","unstructured":"Jia, Z., Ng, M.K., Song, G.J.: Robust quaternion matrix completion with applications to image inpainting. Numerical Linear Algebra with Applications 26(4), e2245 (2019)","journal-title":"Numerical Linear Algebra with Applications"},{"key":"3279_CR25","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2023.108880","volume":"148","author":"P Wu","year":"2024","unstructured":"Wu, P., Kou, K.I., Miao, J.: Efficient low-rank quaternion matrix completion under the learnable transforms for color image recovery. Appl. Math. Lett. 148, 108880 (2024)","journal-title":"Appl. Math. Lett."},{"key":"3279_CR26","doi-asserted-by":"crossref","unstructured":"Sun, J., Liu, X., Zhang, Y.: Quaternion Tensor Completion via QR Decomposition and Nuclear Norm Minimization, Numerical Linear Algebra with Applications, vol. 32, no. 1, (2025)","DOI":"10.1002\/nla.2608"},{"key":"3279_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2024.128823","volume":"615","author":"J Han","year":"2025","unstructured":"Han, J., Kou, K.I., Miao, J., Liu, L., Li, H.: $$L_{2, 1}$$-norm regularized quaternion matrix completion using sparse representation and approximate QSVD. Neurocomputing 615, 128823 (2025)","journal-title":"Neurocomputing"},{"issue":"7","key":"3279_CR28","doi-asserted-by":"publisher","first-page":"9297","DOI":"10.1109\/TNNLS.2022.3232532","volume":"35","author":"Q Liu","year":"2024","unstructured":"Liu, Q., Xiao, L., Huang, N., Tang, J.: Composite neighbor-aware convolutional metric networks for hyperspectral image classification. IEEE Transactions on Neural Networks and Learning Systems 35(7), 9297\u20139311 (2024)","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"3279_CR29","doi-asserted-by":"crossref","unstructured":"Wang, S., Zhang, H., Shen, X., Wang, D., Yu, X.: Blind Bitstream-corrupted Video Recovery via Metadata-guided Diffusion Model, In Proceedings of the Computer Vision and Pattern Recognition Conference, pp. 22975\u201322984, (2025)","DOI":"10.1109\/CVPR52734.2025.02139"},{"issue":"5","key":"3279_CR30","doi-asserted-by":"publisher","first-page":"3351","DOI":"10.1109\/TPAMI.2023.3341688","volume":"46","author":"Y Luo","year":"2023","unstructured":"Luo, Y., Zhao, X., Li, Z., Ng, M.K., Meng, D.: Low-rank tensor function representation for multi-dimensional data recovery. IEEE Trans. Pattern Anal. Mach. Intell. 46(5), 3351\u20133369 (2023)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"3279_CR31","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1109\/TSIPN.2023.3276687","volume":"9","author":"K Pena-Pena","year":"2023","unstructured":"Pena-Pena, K., Lau, D.L., Arce, G.R.: T-HGSP: Hypergraph signal processing using t-product tensor decompositions. IEEE Transactions on Signal and Information Processing over Networks 9, 329\u2013345 (2023)","journal-title":"IEEE Transactions on Signal and Information Processing over Networks"},{"key":"3279_CR32","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1109\/JSTARS.2024.3492177","volume":"18","author":"A Li","year":"2025","unstructured":"Li, A., Jiang, M., Chu, D., Guan, X., Li, J., Shen, H.: Efficient and Effective NDVI Time-Series Reconstruction by Combining Deep Learning and Tensor Completion. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 18, 191\u2013205 (2025)","journal-title":"IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing"},{"key":"3279_CR33","doi-asserted-by":"publisher","unstructured":"Hongo, S., Isokawa, T., Matsui, N., Nishimura, H., Kamiura, N.: Constructing convolutional neural networks based on quaternion. In: 2020 International Joint Conference on Neural Networks (IJCNN), pp. 1\u20136., Glasgow, UK (2020). https:\/\/doi.org\/10.1109\/IJCNN48605.2020.9207325","DOI":"10.1109\/IJCNN48605.2020.9207325"},{"issue":"20","key":"3279_CR34","doi-asserted-by":"publisher","first-page":"31285","DOI":"10.1007\/s11042-023-14688-4","volume":"82","author":"S Singh","year":"2023","unstructured":"Singh, S., Tripathi, B.K., Rawat, S.S.: Deep quaternion convolutional neural networks for breast Cancer classification. Multimedia Tools and Applications 82(20), 31285\u201331308 (2023)","journal-title":"Multimedia Tools and Applications"},{"key":"3279_CR35","doi-asserted-by":"crossref","unstructured":"Grassucci, E., Comminiello, D., Uncini, A.: A quaternion-valued variational autoencoder, In ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). vol.\u00a02021, pp. 3310\u20133314, (2021)","DOI":"10.1109\/ICASSP39728.2021.9413859"},{"key":"3279_CR36","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1109\/LSP.2024.3504374","volume":"32","author":"H Luo","year":"2025","unstructured":"Luo, H., Liu, X., Sun, J., Zhang, Y.: Quaternion Vector Quantized Variational Autoencoder. IEEE Signal Process. Lett. 32, 151\u2013155 (2025)","journal-title":"IEEE Signal Process. Lett."},{"issue":"3","key":"3279_CR37","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1137\/07070111X","volume":"51","author":"TG Kolda","year":"2009","unstructured":"Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455\u2013500 (2009)","journal-title":"SIAM Rev."},{"key":"3279_CR38","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1016\/j.laa.2010.09.020","volume":"43","author":"ME Kilmer","year":"2011","unstructured":"Kilmer, M.E., Martin, C.D.: Factorization strategies for third-order tensors. Linear Algebra Appl. 43, 641\u2013658 (2011)","journal-title":"Linear Algebra Appl."},{"key":"3279_CR39","doi-asserted-by":"crossref","unstructured":"Lu, C., Feng, J., Chen, Y., Liu, W., Lin, Z., Yan, S.: Tensor robust principal component analysis: Exact recovery of corrupted low-rank tensors via convex optimization. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5249\u20135257. (2016)","DOI":"10.1109\/CVPR.2016.567"},{"key":"3279_CR40","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2021.107597","volume":"123","author":"ZZ Qin","year":"2022","unstructured":"Qin, Z.Z., Ming, Z.Y., Zhang, L.P.: Singular value decomposition of third order quaternion tensors. Appl. Math. Lett. 123, 107597 (2022)","journal-title":"Appl. Math. Lett."},{"issue":"5","key":"3279_CR41","doi-asserted-by":"publisher","first-page":"1285","DOI":"10.1007\/s11590-023-02068-8","volume":"18","author":"M Bagherian","year":"2024","unstructured":"Bagherian, M.: Tensor denoising via dual schatten norms. Optimization Letters 18(5), 1285\u20131301 (2024)","journal-title":"Optimization Letters"},{"issue":"2","key":"3279_CR42","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s10915-024-02496-3","volume":"99","author":"CE Yu","year":"2024","unstructured":"Yu, C.E., Liu, X., Zhang, Y.: A new complex structure-preserving method for QSVD. J. Sci. Comput. 99(2), 37 (2024)","journal-title":"J. Sci. Comput."},{"issue":"11","key":"3279_CR43","doi-asserted-by":"publisher","first-page":"27725","DOI":"10.3934\/math.20231419","volume":"8","author":"XH Li","year":"2023","unstructured":"Li, X.H., Liu, X., Jiang, J., Sun, J.: Some solutions to a third-order quaternion tensor equation. AIMS Mathematics 8(11), 27725\u201327741 (2023)","journal-title":"AIMS Mathematics"},{"key":"3279_CR44","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2024.111322","volume":"154","author":"L Yang","year":"2024","unstructured":"Yang, L., Kou, K.I., Miao, J., Liu, Y., Hoi, P.M.: Quaternion tensor completion with sparseness for color video recovery. Appl. Soft Comput. 154, 111322 (2024)","journal-title":"Appl. Soft Comput."},{"key":"3279_CR45","unstructured":"Bertsekas, D.P.: Constrained optimization and Lagrange multiplier methods, Academic press (2014)"},{"issue":"2","key":"3279_CR46","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1287\/moor.1.2.97","volume":"1","author":"RT Rockafellar","year":"1976","unstructured":"Rockafellar, R.T.: Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math. Oper. Res. 1(2), 97\u2013116 (1976)","journal-title":"Math. Oper. Res."},{"key":"3279_CR47","doi-asserted-by":"crossref","unstructured":"Tyrrell Rockafellar, R.: Convex analysis. Princeton mathematical series, p. 28. (1970)","DOI":"10.1515\/9781400873173"},{"key":"3279_CR48","doi-asserted-by":"publisher","first-page":"941","DOI":"10.1007\/s10915-019-01044-8","volume":"81","author":"M Ding","year":"2019","unstructured":"Ding, M., Huang, T.Z., Ji, T.Y., Zhao, X.L., Yang, J.H.: Low-rank tensor completion using matrix factorization based on tensor train rank and total variation. J. Sci. Comput. 81, 941\u2013964 (2019)","journal-title":"J. Sci. Comput."},{"issue":"9","key":"3279_CR49","doi-asserted-by":"publisher","first-page":"2144","DOI":"10.3390\/math11092144","volume":"11","author":"JF Chen","year":"2023","unstructured":"Chen, J.F., Wang, Q.W., Song, G.J., Li, T.: Quaternion matrix factorization for low-rank quaternion matrix completion. Mathematics 11(9), 2144 (2023)","journal-title":"Mathematics"},{"key":"3279_CR50","doi-asserted-by":"crossref","unstructured":"Miao, J., Kou, K.I., Yang, L., Cheng, D.: Quaternion tensor train rank minimization with sparse regularization in a transformed domain for quaternion tensor completion. Knowl.-Based Syst, vol. 284, p. 111222. (2024)","DOI":"10.1016\/j.knosys.2023.111222"},{"key":"3279_CR51","doi-asserted-by":"crossref","unstructured":"Fukuchi, K., Miyazato, K., Kimura, A., Takagi, S., Yamato, J.: Saliency-based video segmentation with graph cuts and sequentially updated priors, in 2009 IEEE International Conference on Multimedia and Expo. IEEE, pp. 638\u2013641, (2009)","DOI":"10.1109\/ICME.2009.5202577"},{"key":"3279_CR52","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1007\/s11263-011-0512-5","volume":"100","author":"D Tsai","year":"2012","unstructured":"Tsai, D., Flagg, M., Nakazawa, A., Rehg, J.M.: Motion coherent tracking using multi-label MRF optimization. Int. J. Comput. Vision 100, 190\u2013202 (2012)","journal-title":"Int. J. Comput. Vision"},{"key":"3279_CR53","unstructured":"Dem\u0161ar, J.: \u201cStatistical comparisons of classifiers over multiple data sets\u201d, Journal of Machine learning research, pp. 1\u201330, (2006)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-026-03279-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-026-03279-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-026-03279-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,11]],"date-time":"2026-08-11T01:50:28Z","timestamp":1786413028000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-026-03279-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,29]]},"references-count":53,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,9]]}},"alternative-id":["3279"],"URL":"https:\/\/doi.org\/10.1007\/s10915-026-03279-8","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,29]]},"assertion":[{"value":"15 December 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 March 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 July 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors have not disclosed any competing interests.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"96"}}