{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,17]],"date-time":"2025-05-17T04:06:48Z","timestamp":1747454808258,"version":"3.40.5"},"publisher-location":"Cham","reference-count":37,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031923654"},{"type":"electronic","value":"9783031923661"}],"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_12","type":"book-chapter","created":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T03:58:23Z","timestamp":1747367903000},"page":"146-158","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Product of\u00a0Gaussian Mixture Diffusion Model for\u00a0Non-linear MRI Inversion"],"prefix":"10.1007","author":[{"given":"Laurenz","family":"Nagler","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1941-875X","authenticated-orcid":false,"given":"Martin","family":"Zach","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6120-1058","authenticated-orcid":false,"given":"Thomas","family":"Pock","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,17]]},"reference":[{"key":"12_CR1","doi-asserted-by":"crossref","unstructured":"Block, K.T., Uecker, M., Frahm, J.: Undersampled radial MRI with multiple coils. iterative image reconstruction using a total variation constraint. Magn. Reson. Med. 57(6), 1086\u20131098 (2007)","DOI":"10.1002\/mrm.21236"},{"issue":"3","key":"12_CR2","doi-asserted-by":"publisher","first-page":"1003","DOI":"10.1137\/21M1455887","volume":"4","author":"L Bogensperger","year":"2022","unstructured":"Bogensperger, L., Chambolle, A., Pock, T.: Convergence of a piggyback-style method for the differentiation of solutions of standard saddle-point problems. SIAM J. Math. Data Sci. 4(3), 1003\u20131030 (2022)","journal-title":"SIAM J. Math. Data Sci."},{"issue":"6","key":"12_CR3","doi-asserted-by":"publisher","first-page":"1256","DOI":"10.1109\/TPAMI.2016.2596743","volume":"39","author":"Y Chen","year":"2017","unstructured":"Chen, Y., Pock, T.: Trainable nonlinear reaction diffusion: a flexible framework for fast and effective image restoration. IEEE Trans. Pattern Anal. Mach. Intell. 39(6), 1256\u20131272 (2017)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"12_CR4","doi-asserted-by":"crossref","unstructured":"Chung, H., Kim, J., Kim, S., Ye, J.C.: Parallel diffusion models of operator and image for blind inverse problems. In: IEEE\/CVF Conference on Computer Vision and Pattern Recognition (2023)","DOI":"10.1109\/CVPR52729.2023.00587"},{"key":"12_CR5","unstructured":"Chung, H., Kim, J., Mccann, M.T., Klasky, M.L., Ye, J.C.: Diffusion posterior sampling for general noisy inverse problems. In: International Conference on Learning Representations (2023)"},{"key":"12_CR6","doi-asserted-by":"crossref","unstructured":"Chung, H., Sim, B., Ye, J.C.: Come-closer-diffuse-faster: accelerating conditional diffusion models for inverse problems through stochastic contraction. In: 2022 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 12403\u201312412 (2021)","DOI":"10.1109\/CVPR52688.2022.01209"},{"key":"12_CR7","doi-asserted-by":"publisher","DOI":"10.1016\/j.media.2022.102479","volume":"80","author":"H Chung","year":"2022","unstructured":"Chung, H., Ye, J.C.: Score-based diffusion models for accelerated MRI. Med. Image Anal. 80, 102479 (2022)","journal-title":"Med. Image Anal."},{"key":"12_CR8","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/978-3-319-12385-1_7","volume-title":"Handbook of Uncertainty Quantification","author":"M Dashti","year":"2017","unstructured":"Dashti, M., Stuart, A.M.: The bayesian approach to inverse problems. In: Ghanem, R., Higdon, D., Owhadi, H. (eds.) Handbook of Uncertainty Quantification, pp. 311\u2013428. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-12385-1_7"},{"key":"12_CR9","unstructured":"Erlacher, M., Zach, M.: Joint non-linear mri inversion with diffusion priors (2023). https:\/\/arxiv.org\/abs\/2310.14842"},{"issue":"6","key":"12_CR10","doi-asserted-by":"publisher","first-page":"1202","DOI":"10.1002\/mrm.10171","volume":"47","author":"MA Griswold","year":"2002","unstructured":"Griswold, M.A., et al.: Generalized autocalibrating partially parallel acquisitions (grappa). Magn. Reson. Med. 47(6), 1202\u20131210 (2002)","journal-title":"Magn. Reson. Med."},{"key":"12_CR11","unstructured":"Hu, Y., Peng, A., Gan, W., Kamilov, U.S.: Adobi: adaptive diffusion bridge for blind inverse problems with application to mri reconstruction (2024)"},{"key":"12_CR12","unstructured":"Huang, J., Mumford, D.: Statistics of natural images and models. In: Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149), vol.\u00a01, pp. 541\u2013547 (1999)"},{"key":"12_CR13","first-page":"14938","volume":"34","author":"A Jalal","year":"2021","unstructured":"Jalal, A., Arvinte, M., Daras, G., Price, E., Dimakis, A.G., Tamir, J.: Robust compressed sensing MRI with deep generative priors. Adv. Neural. Inf. Process. Syst. 34, 14938\u201314954 (2021)","journal-title":"Adv. Neural. Inf. Process. Syst."},{"issue":"2","key":"12_CR14","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1002\/mrm.22595","volume":"65","author":"F Knoll","year":"2011","unstructured":"Knoll, F., Bredies, K., Pock, T., Stollberger, R.: Second order total generalized variation (TGV) for MRI. Magn. Reson. Med. 65(2), 480\u2013491 (2011)","journal-title":"Magn. Reson. Med."},{"key":"12_CR15","doi-asserted-by":"crossref","unstructured":"Knoll, F., et al.: fastmri: a publicly available raw k-space and dicom dataset of knee images for accelerated mr image reconstruction using machine learning. Radiol. Artif. Intell. 2, e190007 (2020)","DOI":"10.1148\/ryai.2020190007"},{"key":"12_CR16","doi-asserted-by":"crossref","unstructured":"Kutyniok, G., Labate, D.: Introduction to Shearlets, pp. 1\u201338. Birkh\u00e4user Boston (2012)","DOI":"10.1007\/978-0-8176-8316-0_1"},{"issue":"5","key":"12_CR17","doi-asserted-by":"publisher","first-page":"2056","DOI":"10.1109\/TIP.2013.2244223","volume":"22","author":"WQ Lim","year":"2013","unstructured":"Lim, W.Q.: Nonseparable shearlet transform. IEEE Trans. Image Process. 22(5), 2056\u20132065 (2013). https:\/\/doi.org\/10.1109\/TIP.2013.2244223","journal-title":"IEEE Trans. Image Process."},{"key":"12_CR18","unstructured":"Luo, G., Heide, M., Uecker, M.: Mri reconstruction via data driven markov chain with joint uncertainty estimation. arXiv preprint arXiv:2202.01479 (2022)"},{"issue":"6","key":"12_CR19","doi-asserted-by":"publisher","first-page":"1182","DOI":"10.1002\/mrm.21391","volume":"58","author":"M Lustig","year":"2007","unstructured":"Lustig, M., Donoho, D., Pauly, J.M.: Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 58(6), 1182\u20131195 (2007)","journal-title":"Magn. Reson. Med."},{"key":"12_CR20","doi-asserted-by":"crossref","unstructured":"Narnhofer, D., Hammernik, K., Knoll, F., Pock, T.: Inverse gans for accelerated MRI reconstruction. In: Wavelets and Sparsity XVIII (2019), sPIE Optics+Photonics 2019, 23\u201327 Aug 2019 (2019)","DOI":"10.1117\/12.2527753"},{"key":"12_CR21","first-page":"543","volume":"269","author":"Y Nesterov","year":"1983","unstructured":"Nesterov, Y.: A method for solving the convex programming problem with convergence rate o(1\/$$k^2$$). Proc. USSR Acad. Sci. 269, 543\u2013547 (1983)","journal-title":"Proc. USSR Acad. Sci."},{"issue":"5","key":"12_CR22","doi-asserted-by":"publisher","first-page":"952","DOI":"10.1002\/(SICI)1522-2594(199911)42:5<952::AID-MRM16>3.0.CO;2-S","volume":"42","author":"KP Pruessmann","year":"1999","unstructured":"Pruessmann, K.P., Weiger, M., Scheidegger, M.B., Boesiger, P.: Sense: sensitivity encoding for fast MRI. Magn. Reson. Med. 42(5), 952\u2013962 (1999)","journal-title":"Magn. Reson. Med."},{"key":"12_CR23","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61544-3","volume-title":"The Fokker-Planck Equation: Methods of Solution and Applications","author":"H Risken","year":"1996","unstructured":"Risken, H.: The Fokker-Planck Equation: Methods of Solution and Applications. Springer, Heidelberg (1996)"},{"key":"12_CR24","unstructured":"Salimans, T., Ho, J.: Should EBMs model the energy or the score? In: Energy Based Models Workshop - ICLR 2021 (2021)"},{"key":"12_CR25","unstructured":"Shah, K., Chen, S., Klivans, A.R.: Learning mixtures of gaussians using the ddpm objective (2023)"},{"key":"12_CR26","unstructured":"Song, Y., Ermon, S.: Generative modeling by estimating gradients of the data distribution. Adv. Neural Inf. Process. Syst., 11895\u201311907 (2019)"},{"key":"12_CR27","unstructured":"Song, Y., Shen, L., Xing, L., Ermon, S.: Solving inverse problems in medical imaging with score-based generative models. In: International Conference on Learning Representations (2022)"},{"key":"12_CR28","unstructured":"Song, Y., Sohl-Dickstein, J., Kingma, D.P., Kumar, A., Ermon, S., Poole, B.: Score-based generative modeling through stochastic differential equations. In: International Conference on Learning Representations (2021)"},{"key":"12_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1007\/978-3-030-59713-9_7","volume-title":"Medical Image Computing and Computer Assisted Intervention \u2013 MICCAI 2020","author":"A Sriram","year":"2020","unstructured":"Sriram, A., et al.: End-to-End variational networks for accelerated MRI reconstruction. In: Martel, A.L., et al. (eds.) MICCAI 2020. LNCS, vol. 12262, pp. 64\u201373. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-59713-9_7"},{"issue":"3","key":"12_CR30","doi-asserted-by":"publisher","first-page":"674","DOI":"10.1002\/mrm.21691","volume":"60","author":"M Uecker","year":"2008","unstructured":"Uecker, M., Hohage, T., Block, K.T., Frahm, J.: Image reconstruction by regularized nonlinear inversion-joint estimation of coil sensitivities and image content. Magn. Reson. Med. 60(3), 674\u2013682 (2008)","journal-title":"Magn. Reson. Med."},{"issue":"3","key":"12_CR31","doi-asserted-by":"publisher","first-page":"990","DOI":"10.1002\/mrm.24751","volume":"71","author":"M Uecker","year":"2014","unstructured":"Uecker, M., et al.: Espirit an eigenvalue approach to autocalibrating parallel MRI: where sense meets grappa. Magn. Reson. Med. 71(3), 990\u20131001 (2014)","journal-title":"Magn. Reson. Med."},{"key":"12_CR32","doi-asserted-by":"publisher","first-page":"1661","DOI":"10.1162\/NECO_a_00142","volume":"23","author":"P Vincent","year":"2011","unstructured":"Vincent, P.: A connection between score matching and denoising autoencoders. Neural Comput. 23, 1661\u20131674 (2011)","journal-title":"Neural Comput."},{"key":"12_CR33","doi-asserted-by":"crossref","unstructured":"Zach, M., Knoll, F., Pock, T.: Stable deep MRI reconstruction using generative priors. IEEE Trans. Med. Imaging (2023)","DOI":"10.1109\/TMI.2023.3311345"},{"key":"12_CR34","doi-asserted-by":"crossref","unstructured":"Zach, M., Kobler, E., Chambolle, A., Pock, T.: Product of gaussian mixture diffusion models. J. Math. Imaging Vision 66, 1\u201325 (2024)","DOI":"10.1007\/s10851-024-01180-3"},{"key":"12_CR35","unstructured":"Zbontar, J., et al.: fastmri: an open dataset and benchmarks for accelerated MRI (2019)"},{"key":"12_CR36","doi-asserted-by":"publisher","first-page":"1236","DOI":"10.1109\/34.632983","volume":"19","author":"S Zhu","year":"1997","unstructured":"Zhu, S., Mumford, D.: Prior learning and Gibbs reaction-diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 19, 1236\u20131250 (1997)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"12_CR37","unstructured":"Zhuang, J., et al.: Adabelief optimizer: adapting stepsizes by the belief in observed gradients. In: Conference on Neural Information Processing Systems (2020)"}],"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_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T11:50:54Z","timestamp":1747396254000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-92366-1_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031923654","9783031923661"],"references-count":37,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-92366-1_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"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"}}]}}