{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T19:21:40Z","timestamp":1783970500359,"version":"3.55.0"},"reference-count":60,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T00:00:00Z","timestamp":1717459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T00:00:00Z","timestamp":1717459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-19-CHIA-0017-01-DEEP-VISION"],"award-info":[{"award-number":["ANR-19-CHIA-0017-01-DEEP-VISION"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2024,8]]},"DOI":"10.1007\/s10851-024-01191-0","type":"journal-article","created":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T13:10:44Z","timestamp":1717506644000},"page":"584-605","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Convergence and Recovery Guarantees of Unsupervised Neural Networks for Inverse Problems"],"prefix":"10.1007","volume":"66","author":[{"given":"Nathan","family":"Buskulic","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jalal","family":"Fadili","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yvain","family":"Qu\u00e9au","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,6,4]]},"reference":[{"key":"1191_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492919000059","volume":"28","author":"S Arridge","year":"2019","unstructured":"Arridge, S., Maass, P., Ozan, O., Sch\u00f6nlieb, C.B.: Solving inverse problems using data-driven models. Acta. Numer. 28, 1\u2013174 (2019)","journal-title":"Acta. Numer."},{"key":"1191_CR2","doi-asserted-by":"crossref","unstructured":"Ongie, G., Jalal, A., Metzler, C.A., Baraniuk, R.G., Dimakis, A.G., Willett, R.: Deep learning techniques for inverse problems in imaging. IEEE J. Selected Areas Inf. Theory, 39\u201356 (2020)","DOI":"10.1109\/JSAIT.2020.2991563"},{"issue":"1","key":"1191_CR3","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1109\/MSP.2022.3207451","volume":"40","author":"S Mukherjee","year":"2023","unstructured":"Mukherjee, S., Hauptmann, A., \u00d6ktem, O., Pereyra, M., Sch\u00f6nlieb, C.-B.: Learned reconstruction methods with convergence guarantees: a survey of concepts and applications. IEEE Signal Process. Mag. 40(1), 164\u2013182 (2023)","journal-title":"IEEE Signal Process. Mag."},{"issue":"6","key":"1191_CR4","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ab6d57","volume":"36","author":"H Li","year":"2020","unstructured":"Li, H., Schwab, J., Antholzer, S., Haltmeier, M.: NETT: solving inverse problems with deep neural networks. Inverse Prob. 36(6), 065005 (2020)","journal-title":"Inverse Prob."},{"key":"1191_CR5","unstructured":"Mukherjee, S., Dittmer, S., Shumaylov, Z., Lunz, S., \u00d6ktem, O., Sch\u00f6nlieb, C.-B.: Learned convex regularizers for inverse problems. arXiv preprint arXiv:2008.02839 (2020)"},{"issue":"2","key":"1191_CR6","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/aaf14a","volume":"35","author":"J Schwab","year":"2019","unstructured":"Schwab, J., Antholzer, S., Haltmeier, M.: Deep null space learning for inverse problems: convergence analysis and rates. Inverse Prob. 35(2), 025008 (2019)","journal-title":"Inverse Prob."},{"key":"1191_CR7","first-page":"5921","volume":"34","author":"J Liu","year":"2021","unstructured":"Liu, J., Asif, S., Wohlberg, B., Kamilov, U.: Recovery analysis for plug-and-play priors using the restricted eigenvalue condition. Adv. Neural. Inf. Process. Syst. 34, 5921\u20135933 (2021)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"key":"1191_CR8","doi-asserted-by":"crossref","unstructured":"Ulyanov, D., Vedaldi, A., Lempitsky, V.: Deep image prior. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 9446\u20139454 (2018)","DOI":"10.1109\/CVPR.2018.00984"},{"key":"1191_CR9","doi-asserted-by":"crossref","unstructured":"Prost, J., Houdard, A., Almansa, A., Papadakis, N.: Learning local regularization for variational image restoration. In: International Conference on Scale Space and Variational Methods in Computer Vision, pp. 358\u2013370 (2021)","DOI":"10.1007\/978-3-030-75549-2_29"},{"key":"1191_CR10","doi-asserted-by":"crossref","unstructured":"Venkatakrishnan, S.V., Bouman, C.A., Wohlberg, B.: Plug-and-play priors for model based reconstruction. In: 2013 IEEE Global Conference on Signal and Information Processing, pp. 945\u2013948 (2013)","DOI":"10.1109\/GlobalSIP.2013.6737048"},{"issue":"2","key":"1191_CR11","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1109\/MSP.2020.3016905","volume":"38","author":"V Monga","year":"2021","unstructured":"Monga, V., Li, Y., Eldar, Y.C.: Algorithm unrolling: interpretable, efficient deep learning for signal and image processing. IEEE Signal Process. Mag. 38(2), 18\u201344 (2021)","journal-title":"IEEE Signal Process. Mag."},{"key":"1191_CR12","doi-asserted-by":"crossref","unstructured":"Liu, J., Sun, Y., Xu, X., Kamilov, U.S.: Image restoration using total variation regularized deep image prior. In: ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 7715\u20137719 (2019)","DOI":"10.1109\/ICASSP.2019.8682856"},{"key":"1191_CR13","unstructured":"Mataev, G., Milanfar, P., Elad, M.: Deepred: Deep image prior powered by red. In: Proceedings of the IEEE\/CVF International Conference on Computer Vision Workshops, (2019)"},{"issue":"4","key":"1191_CR14","doi-asserted-by":"publisher","first-page":"885","DOI":"10.1007\/s11263-021-01572-7","volume":"130","author":"Z Shi","year":"2022","unstructured":"Shi, Z., Mettes, P., Maji, S., Snoek, C.G.: On measuring and controlling the spectral bias of the deep image prior. Int. J. Comput. Vis. 130(4), 885\u2013908 (2022)","journal-title":"Int. J. Comput. Vis."},{"key":"1191_CR15","doi-asserted-by":"crossref","unstructured":"Zukerman, J., Tirer, T., Giryes, R.: Bp-dip: A backprojection based deep image prior. In: 2020 28th European Signal Processing Conference (EUSIPCO), pp. 675\u2013679 (2021). IEEE","DOI":"10.23919\/Eusipco47968.2020.9287540"},{"key":"1191_CR16","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1017\/S0962492921000027","volume":"30","author":"PL Bartlett","year":"2021","unstructured":"Bartlett, P.L., Montanari, A., Rakhlin, A.: Deep learning: a statistical viewpoint. Acta. Numer. 30, 87\u2013201 (2021)","journal-title":"Acta. Numer."},{"issue":"5","key":"1191_CR17","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1109\/JPROC.2020.3048020","volume":"109","author":"C Fang","year":"2021","unstructured":"Fang, C., Dong, H., Zhang, T.: Mathematical models of overparameterized neural networks. Proc. IEEE 109(5), 683\u2013703 (2021)","journal-title":"Proc. IEEE"},{"key":"1191_CR18","unstructured":"Chizat, L., Oyallon, E., Bach, F.: On lazy training in differentiable programming. Adv. Neural Inf. Process. Syst. 32 (2019)"},{"key":"1191_CR19","unstructured":"Du, S.S., Zhai, X., Poczos, B., Singh, A.: Gradient descent provably optimizes over-parameterized neural networks. In: International Conference on Learning Representations (2019)"},{"key":"1191_CR20","unstructured":"Arora, S., Du, S., Hu, W., Li, Z., Wang, R.: Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks. In: International Conference on Machine Learning, pp. 322\u2013332 (2019)"},{"key":"1191_CR21","unstructured":"Oymak, S., Soltanolkotabi, M.: Overparameterized nonlinear learning: gradient descent takes the shortest path? In: International Conference on Machine Learning, pp. 4951\u20134960 (2019)"},{"issue":"1","key":"1191_CR22","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1109\/JSAIT.2020.2991332","volume":"1","author":"S Oymak","year":"2020","unstructured":"Oymak, S., Soltanolkotabi, M.: Toward moderate overparameterization: global convergence guarantees for training shallow neural networks. IEEE J. Selected Areas Inf. Theory 1(1), 84\u2013105 (2020)","journal-title":"IEEE J. Selected Areas Inf. Theory"},{"key":"1191_CR23","unstructured":"Lojasiewicz, S.: Une propri\u00e9t\u00e9 topologique des sous-ensembles analytiques r\u00e9els. Coll. du CNRS, Les \u00e9quations aux d\u00e9riv\u00e9es partielles 117(87-89), 2 (1963)"},{"key":"1191_CR24","unstructured":"\u0141ojasiewicz, S.: Sur les trajectoires du gradient d\u2019une fonction analytique. Semin. Geom., Univ. Studi Bologna 1982\/1983, 115\u2013117 (1984)"},{"key":"1191_CR25","doi-asserted-by":"crossref","unstructured":"Kurdyka, K.: On gradients of functions definable in o-minimal structures. In: Annales de L\u2019institut Fourier, vol. 48, pp. 769\u2013783 (1998). Issue: 3","DOI":"10.5802\/aif.1638"},{"key":"1191_CR26","unstructured":"Jacot, A., Gabriel, F., Hongler, C.: Neural tangent kernel: Convergence and generalization in neural networks. Advances in neural information processing systems 31 (2018)"},{"key":"1191_CR27","unstructured":"Rahimi, A., Recht, B.: Weighted sums of random kitchen sinks: replacing minimization with randomization in learning. Adv. Neural Inf. Process. Syst. 21 (2008)"},{"key":"1191_CR28","doi-asserted-by":"crossref","unstructured":"Buskulic, N., Qu\u00e9au, Y., Fadili, J.: Convergence guarantees of overparametrized wide deep inverse prior. In: International Conference on Scale Space and Variational Methods in Computer Vision, pp. 406\u2013417 (2023)","DOI":"10.1007\/978-3-031-31975-4_31"},{"issue":"6","key":"1191_CR29","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1037\/h0042519","volume":"65","author":"F Rosenblatt","year":"1958","unstructured":"Rosenblatt, F.: The perceptron: a probabilistic model for information storage and organization in the brain. Psychol. Rev. 65(6), 386 (1958)","journal-title":"Psychol. Rev."},{"issue":"1","key":"1191_CR30","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/s10107-006-0706-8","volume":"108","author":"Y Nesterov","year":"2006","unstructured":"Nesterov, Y., Polyak, B.T.: Cubic regularization of newton method and its global performance. Math. Program. 108(1), 177\u2013205 (2006)","journal-title":"Math. Program."},{"issue":"2","key":"1191_CR31","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1137\/040605266","volume":"16","author":"PA Absil","year":"2005","unstructured":"Absil, P.A., Mahony, R., Andrews, B.: Convergence of the iterates of descent methods for analytic cost functions. SIAM J. Optim. 16(2), 531\u2013547 (2005)","journal-title":"SIAM J. Optim."},{"key":"1191_CR32","unstructured":"Huang, S.Z.: Gradient inequalities. With applications to asymptotic behavior and stability of gradient-like systems. Mathematical Surveys and Monographs, vol. 126. American Mathematical Society, Providence, RI (2006)"},{"issue":"4","key":"1191_CR33","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.1137\/050644641","volume":"17","author":"J Bolte","year":"2007","unstructured":"Bolte, J., Daniilidis, A., Lewis, A.: The \u0142ojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems. SIAM J. Optim. 17(4), 1205\u20131223 (2007)","journal-title":"SIAM J. Optim."},{"issue":"1","key":"1191_CR34","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10107-007-0133-5","volume":"116","author":"H Attouch","year":"2009","unstructured":"Attouch, H., Bolte, J.: On the convergence of the proximal algorithm for nonsmooth functions involving analytic features. Math. Program. 116(1), 5\u201316 (2009)","journal-title":"Math. Program."},{"issue":"2","key":"1191_CR35","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1287\/moor.1100.0449","volume":"35","author":"H Attouch","year":"2010","unstructured":"Attouch, H., Bolte, J., Redont, P., Soubeyran, A.: Proximal alternating minimization and projection methods for nonconvex problems: an approach based on the kurdyka-\u0142ojasiewicz inequality. Math. Oper. Res. 35(2), 438\u2013457 (2010)","journal-title":"Math. Oper. Res."},{"issue":"6","key":"1191_CR36","doi-asserted-by":"publisher","first-page":"3319","DOI":"10.1090\/S0002-9947-09-05048-X","volume":"362","author":"J Bolte","year":"2010","unstructured":"Bolte, J., Daniilidis, A., Ley, O., Mazet, L.: Characterizations of \u0142ojasiewicz inequalities: subgradient flows, talweg, convexity. Trans. Am. Math. Soc. 362(6), 3319\u20133363 (2010)","journal-title":"Trans. Am. Math. Soc."},{"issue":"6","key":"1191_CR37","doi-asserted-by":"publisher","first-page":"1471","DOI":"10.1109\/TNN.2006.879775","volume":"17","author":"M Forti","year":"2006","unstructured":"Forti, M., Nistri, P., Quincampoix, M.: Convergence of neural networks for programming problems via a nonsmooth \u0142ojasiewicz inequality. IEEE Trans. Neural Networks 17(6), 1471\u20131486 (2006)","journal-title":"IEEE Trans. Neural Networks"},{"issue":"3","key":"1191_CR38","doi-asserted-by":"publisher","first-page":"525","DOI":"10.2307\/2006981","volume":"118","author":"L Simon","year":"1983","unstructured":"Simon, L.: Asymptotics for a class of non-linear evolution equations, with applications to geometric problems. Ann. Math. 118(3), 525\u2013571 (1983)","journal-title":"Ann. Math."},{"key":"1191_CR39","unstructured":"Haraux, A.: A hyperbolic variant of Simon\u2019s convergence theorem. In: Lumer, G. (ed.) Evolution equations and their applications in physical and life sciences. Lecture Notes in Pure and Appl. Math., vol. 215 (2001)"},{"issue":"2","key":"1191_CR40","doi-asserted-by":"publisher","first-page":"611","DOI":"10.1016\/j.jde.2006.02.009","volume":"228","author":"R Chill","year":"2006","unstructured":"Chill, R., Fiorenza, A.: Convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations. J. Differ. Equ. 228(2), 611\u2013632 (2006)","journal-title":"J. Differ. Equ."},{"key":"1191_CR41","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1007\/s10107-016-1091-6","volume":"165","author":"J Bolte","year":"2017","unstructured":"Bolte, J., Nguyen, T.P., Peypouquet, J., Suter, B.W.: From error bounds to the complexity of first-order descent methods for convex functions. Math. Program. 165, 471\u2013507 (2017)","journal-title":"Math. Program."},{"key":"1191_CR42","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-48311-5","volume-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces","author":"HH Bauschke","year":"2017","unstructured":"Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, Cham (2017)"},{"key":"1191_CR43","volume-title":"An Introduction to O-minimal Geometry","author":"M Coste","year":"2000","unstructured":"Coste, M.: An Introduction to O-minimal Geometry. Istituti editoriali e poligrafici internazionali Pisa, Pisa (2000)"},{"key":"1191_CR44","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511525919","volume-title":"Tame Topology and O-minimal Structures","author":"L Dries","year":"1998","unstructured":"Dries, L.: Tame Topology and O-minimal Structures, vol. 248. Cambridge University Press, Cambridge (1998)"},{"key":"1191_CR45","unstructured":"Scherzer, O., Grasmair, M., Grossauer, H., Haltmeier, M., Lenzen, F.: Variational methods in imaging, 1st edn. Applied Mathematical Sciences. Springer, Cham (2009)"},{"key":"1191_CR46","unstructured":"Haraux, A.: Syst\u00e8mes Dynamiques Dissipatifs et Applications. Recherches en Math\u00e9matiques Appliqu\u00e9es, vol. 17. Masson, Paris (1991)"},{"issue":"48","key":"1191_CR47","doi-asserted-by":"publisher","first-page":"30088","DOI":"10.1073\/pnas.1907377117","volume":"117","author":"V Antun","year":"2020","unstructured":"Antun, V., Renna, F., Poon, C., Adcock, B., Hansen, A.C.: On instabilities of deep learning in image reconstruction and the potential costs of ai. Proc. Natl. Acad. Sci. 117(48), 30088\u201330095 (2020)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"1191_CR48","unstructured":"Gottschling, N.M., Antun, V., Adcock, B., Hansen, A.C.: The troublesome kernel on hallucinations: no free lunches and the accuracy-stability trade-off in inverse problems. arXiv preprint arXiv:2001.01258 (2020)"},{"issue":"6","key":"1191_CR49","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1007\/s10208-012-9135-7","volume":"12","author":"V Chandrasekaran","year":"2012","unstructured":"Chandrasekaran, V., Recht, B., Parrilo, P.A., Willsky, A.: The convex geometry of linear inverse problems. Found. Comput. Math. 12(6), 805\u2013849 (2012)","journal-title":"Found. Comput. Math."},{"key":"1191_CR50","doi-asserted-by":"crossref","unstructured":"Tropp, J.A.: Convex recovery of a structured signal from independent random linear measurements. Sampling theory, a renaissance: compressive sensing and other developments, 67\u2013101 (2015)","DOI":"10.1007\/978-3-319-19749-4_2"},{"key":"1191_CR51","unstructured":"Joshi, B., Li, X., Plan, Y., Yilmaz, O.: Plugin-cs: A simple algorithm for compressive sensing with generative prior. In: NeurIPS 2021 Workshop on Deep Learning and Inverse Problems (2021)"},{"key":"1191_CR52","doi-asserted-by":"crossref","unstructured":"Jagatap, G., Hegde, C.: Algorithmic guarantees for inverse imaging with untrained network priors. Adv. Neural Inf. Processing Syst. 32 (2019)","DOI":"10.31274\/cc-20240624-143"},{"key":"1191_CR53","unstructured":"Khayatkhoei, M., Elgammal, A., Singh, M.: Disconnected manifold learning for generative adversarial networks. In: 32nd International Conference on Neural Information Processing Systems, pp. 7354\u20137364 (2018)"},{"key":"1191_CR54","doi-asserted-by":"crossref","unstructured":"Gurumurthy, S., Kiran\u00a0Sarvadevabhatla, R., Venkatesh\u00a0Babu, R.: Deligan: Generative adversarial networks for diverse and limited data. In: IEEE Conference On Computer Vision and Pattern Recognition, pp. 166\u2013174 (2017)","DOI":"10.1109\/CVPR.2017.525"},{"key":"1191_CR55","unstructured":"Tanielian, U., Issenhuth, T., Dohmatob, E., Mary, J.: Learning disconnected manifolds: a no GAN\u2019s land. In: International Conference on Machine Learning, pp. 9418\u20139427 (2020)"},{"key":"1191_CR56","unstructured":"Salmona, A., Bortoli, V.D., Delon, J., Desolneux, A.: Can push-forward generative models fit multimodal distributions? In: Advances in Neural Information Processing Systems (2022)"},{"key":"1191_CR57","unstructured":"Issenhuth, T., Tanielian, U., Mary, J., Picard, D.: Unveiling the latent space geometry of push-forward generative models. In: Nternational Conference on Machine Learning (2023)"},{"key":"1191_CR58","unstructured":"Pope, P., Zhu, C., Abdelkader, A., Goldblum, M., , Goldstein, T.: he intrinsic dimension of images and its impact on learning. In: International Conference on Learning Representations (2020)"},{"issue":"8","key":"1191_CR59","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/abe928","volume":"37","author":"P Hagemann","year":"2021","unstructured":"Hagemann, P., Neumayer, S.: Stabilizing invertible neural networks using mixture models. Inverse Prob. 37(8), 085002 (2021)","journal-title":"Inverse Prob."},{"key":"1191_CR60","doi-asserted-by":"crossref","unstructured":"Tropp, J.A., et al.: An introduction to matrix concentration inequalities. Foundations and Trends in Machine Learning 8(1-2), 1\u2013230 (2015)","DOI":"10.1561\/2200000048"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-024-01191-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10851-024-01191-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-024-01191-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,21]],"date-time":"2024-11-21T02:40:39Z","timestamp":1732156839000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10851-024-01191-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,4]]},"references-count":60,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,8]]}},"alternative-id":["1191"],"URL":"https:\/\/doi.org\/10.1007\/s10851-024-01191-0","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,4]]},"assertion":[{"value":"15 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 April 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 June 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}