{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T01:25:56Z","timestamp":1768872356761,"version":"3.49.0"},"publisher-location":"Cham","reference-count":24,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031923654","type":"print"},{"value":"9783031923661","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-92366-1_2","type":"book-chapter","created":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T03:58:30Z","timestamp":1747367910000},"page":"16-29","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Denoising Hyperbolic-Valued Data by\u00a0Relaxed Regularizations"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7813-2762","authenticated-orcid":false,"given":"Robert","family":"Beinert","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0009-3855-0933","authenticated-orcid":false,"given":"Jonas","family":"Bresch","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,17]]},"reference":[{"key":"2_CR1","doi-asserted-by":"publisher","unstructured":"Angulo, J., Velasco-Forero, S.: Morphological processing of univariate gaussian distribution-valued images based on Poincar\u00e9 upper-half plane representation. In: Nielsen, F. (ed.) Geometric Theory of Information. SCT, pp. 331\u2013366. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-05317-2_12","DOI":"10.1007\/978-3-319-05317-2_12"},{"key":"2_CR2","doi-asserted-by":"publisher","unstructured":"Atigh, M.G., Schoep, J., Acar, E., Van\u00a0Noord, N., Mettes, P.: Hyperbolic image segmentation. In: Proceedings of the CVPR \u201922, pp. 4443\u20134452 (2022). https:\/\/doi.org\/10.1109\/CVPR52688.2022.00441","DOI":"10.1109\/CVPR52688.2022.00441"},{"key":"2_CR3","doi-asserted-by":"publisher","unstructured":"Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York (2011). https:\/\/doi.org\/10.1007\/978-1-4419-9467-7","DOI":"10.1007\/978-1-4419-9467-7"},{"key":"2_CR4","doi-asserted-by":"publisher","DOI":"10.1002\/pamm.202400016","author":"R Beinert","year":"2024","unstructured":"Beinert, R., Bresch, J.: Denoising sphere-valued data by relaxed total variation regularization. Proc. Appl. Math. Mech. (2024). https:\/\/doi.org\/10.1002\/pamm.202400016","journal-title":"Proc. Appl. Math. Mech."},{"key":"2_CR5","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2024026","author":"R Beinert","year":"2024","unstructured":"Beinert, R., Bresch, J., Steidl, G.: Denoising of sphere- and SO(3)-valued data by relaxed Tikhonov regularization. Inverse Probl. Imaging (2024). https:\/\/doi.org\/10.3934\/ipi.2024026","journal-title":"Inverse Probl. Imaging"},{"issue":"3","key":"2_CR6","doi-asserted-by":"publisher","first-page":"901","DOI":"10.1137\/15M1052858","volume":"9","author":"R Bergmann","year":"2016","unstructured":"Bergmann, R., Persch, J., Steidl, G.: A parallel Douglas-Rachford algorithm for minimizing ROF-like functionals on images with values in symmetric Hadamard manifolds. SIAM J. Imaging Sci. 9(3), 901\u2013937 (2016). https:\/\/doi.org\/10.1137\/15M1052858","journal-title":"SIAM J. Imaging Sci."},{"issue":"1","key":"2_CR7","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1038\/ncomms1063","volume":"1","author":"M Bogu\u00f1\u00e1","year":"2010","unstructured":"Bogu\u00f1\u00e1, M., Papadopoulos, F., Krioukov, D.: Sustaining the internet with hyperbolic mapping. Nat. Commun. 1(1), 62 (2010). https:\/\/doi.org\/10.1038\/ncomms1063","journal-title":"Nat. Commun."},{"key":"2_CR8","doi-asserted-by":"publisher","unstructured":"Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004). https:\/\/doi.org\/10.1017\/CBO9780511804441","DOI":"10.1017\/CBO9780511804441"},{"issue":"12","key":"2_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pcbi.1000625","volume":"5","author":"P Chossat","year":"2009","unstructured":"Chossat, P., Faugeras, O.: Hyperbolic planforms in relation to visual edges and textures perception. PLoS Comput. Biol. 5(12), 1\u201316 (2009). https:\/\/doi.org\/10.1371\/journal.pcbi.1000625","journal-title":"PLoS Comput. Biol."},{"key":"2_CR10","doi-asserted-by":"crossref","unstructured":"Condat, L.: A direct algorithm for 1D total variation denoising (2012). https:\/\/hal.science\/hal-00675043","DOI":"10.1109\/LSP.2013.2278339"},{"issue":"11","key":"2_CR11","doi-asserted-by":"publisher","first-page":"1054","DOI":"10.1109\/LSP.2013.2278339","volume":"20","author":"L Condat","year":"2013","unstructured":"Condat, L.: A direct algorithm for 1D total variation denoising. IEEE Signal Process. Lett. 20(11), 1054\u20131057 (2013). https:\/\/doi.org\/10.1109\/LSP.2013.2278339","journal-title":"IEEE Signal Process. Lett."},{"key":"2_CR12","doi-asserted-by":"publisher","unstructured":"Condat, L.: Tikhonov regularization of circle-valued signals. IEEE Trans. Signal Process. 70, 2775\u20132782 (2022). https:\/\/doi.org\/10.1109\/TSP.2022.3179816","DOI":"10.1109\/TSP.2022.3179816"},{"key":"2_CR13","unstructured":"Ganea, O.E., B\u00e9cigneul, G., Hofmann, T.: Hyperbolic neural networks. In: Advances in Neural Information Processing Systems, pp. 5350\u20145360. Curran Associates, New York (2018). https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2018\/file\/dbab2adc8f9d078009ee3fa810bea142-Paper.pdf"},{"key":"2_CR14","doi-asserted-by":"publisher","unstructured":"Glowinski, R., Marroco, A.: Sur l\u2019approximation, par \u00e9l\u00e9ments finis d\u2019ordre un, et la r\u00e9solution, par p\u00e9nalisation-dualit\u00e9 d\u2019une classe de probl\u00e8mes de dirichlet non lin\u00e9aires. R.A.I.R.O. Analyse Num\u00e9rique 9(R2), 41\u201376 (1975). https:\/\/doi.org\/10.1051\/m2an\/197509R200411","DOI":"10.1051\/m2an\/197509R200411"},{"key":"2_CR15","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/BF01206614","volume":"95","author":"H Hopf","year":"1926","unstructured":"Hopf, H.: Zum Clifford-Kleinschen Raumproblem. Math. Ann. 95, 313\u2013339 (1926)","journal-title":"Math. Ann."},{"key":"2_CR16","doi-asserted-by":"publisher","unstructured":"Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge, 2nd edn. (2012). https:\/\/doi.org\/10.1017\/CBO9780511810817","DOI":"10.1017\/CBO9780511810817"},{"key":"2_CR17","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/BF01206655","volume":"39","author":"W Killing","year":"1891","unstructured":"Killing, W.: Ueber die Clifford-Klein\u2019schen Raumformen. Math. Ann. 39, 257\u2013278 (1891)","journal-title":"Math. Ann."},{"key":"2_CR18","doi-asserted-by":"publisher","unstructured":"Krioukov, D., Papadopoulos, F., Kitsak, M., Vahdat, A., Bogu\u00f1\u00e1, M.: Hyperbolic geometry of complex networks. Phys. Rev. E 82, 036106 (2010). https:\/\/doi.org\/10.1103\/PhysRevE.82.036106","DOI":"10.1103\/PhysRevE.82.036106"},{"key":"2_CR19","volume-title":"Statistical Analysis and Optimal Transport for Euclidean and Manifold-Valued Data","author":"FJ Laus","year":"2020","unstructured":"Laus, F.J.: Statistical Analysis and Optimal Transport for Euclidean and Manifold-Valued Data. Dr. Hut, M\u00fcnchen (2020)"},{"key":"2_CR20","doi-asserted-by":"publisher","unstructured":"Lee, J.: Riemannian Manifolds: An Introduction to Curvature. Springer, New York (1997). https:\/\/doi.org\/10.1007\/b98852","DOI":"10.1007\/b98852"},{"key":"2_CR21","doi-asserted-by":"publisher","unstructured":"Lin, F., Bai, B., Guo, Y., Chen, H., Ren, Y., Xu, Z.: MHCN: A hyperbolic neural network model for multi-view hierarchical clustering. In: Proceedings of the ICCV \u201923, pp. 16479\u201316489 (2023). https:\/\/doi.org\/10.1109\/ICCV51070.2023.01515","DOI":"10.1109\/ICCV51070.2023.01515"},{"key":"2_CR22","unstructured":"Liu, Q., Nickel, M., Kiela, D.: Hyperbolic graph neural networks. In: Advances in Neural Information Processing Systems. vol.\u00a032. Curran Associates (2019). https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2019\/file\/103303dd56a731e377d01f6a37badae3-Paper.pdf"},{"key":"2_CR23","unstructured":"Nickel, M., Kiela, D.: Poincar\u00e9 embeddings for learning hierarchical representations. In: Advances in Neural Information Processing Systems, vol.\u00a030. Curran Associates (2017). https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2017\/file\/59dfa2df42d9e3d41f5b02bfc32229dd-Paper.pdf"},{"key":"2_CR24","doi-asserted-by":"publisher","unstructured":"Wald, R.M.: General Relativity. Chicago University Press, Chicago (1984). https:\/\/doi.org\/10.7208\/chicago\/9780226870373.001.0001","DOI":"10.7208\/chicago\/9780226870373.001.0001"}],"container-title":["Lecture Notes in Computer Science","Scale Space and Variational Methods in Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-92366-1_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T11:50:47Z","timestamp":1747396247000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-92366-1_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031923654","9783031923661"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-92366-1_2","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"17 May 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SSVM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Scale Space and Variational Methods in Computer Vision","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Dartington","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Kingdom","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 May 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 May 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"scalespace2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}