{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,23]],"date-time":"2026-05-23T13:07:42Z","timestamp":1779541662947,"version":"3.53.1"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2026,5,23]],"date-time":"2026-05-23T00:00:00Z","timestamp":1779494400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,5,23]],"date-time":"2026-05-23T00:00:00Z","timestamp":1779494400000},"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":["Stat Comput"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1007\/s11222-026-10890-0","type":"journal-article","created":{"date-parts":[[2026,5,23]],"date-time":"2026-05-23T12:52:01Z","timestamp":1779540721000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A persistent-homology-based Bayesian prior for potential coefficient reconstruction in an elliptic partial differential equation"],"prefix":"10.1007","volume":"36","author":[{"given":"Zhiliang","family":"Deng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haiyang","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaofei","family":"Guan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiyuan","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaomei","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,23]]},"reference":[{"issue":"085010","key":"10890_CR1","first-page":"20","volume":"26","author":"G Bal","year":"2010","unstructured":"Bal, G., Uhlmann, G.: Inverse diffusion theory of photoacoustics. Inverse Prob. 26(085010), 20 (2010)","journal-title":"Inverse Prob."},{"issue":"2","key":"10890_CR2","doi-asserted-by":"publisher","first-page":"103","DOI":"10.3934\/fods.2019005","volume":"1","author":"M Banterle","year":"2019","unstructured":"Banterle, M., Granzian, C., Lee, A., Robert, C.P.: Accelerating metropolis-hastings algorithms by delayed acceptance. Foundations of Data Science 1(2), 103\u2013128 (2019)","journal-title":"Foundations of Data Science"},{"issue":"2","key":"10890_CR3","doi-asserted-by":"publisher","first-page":"397","DOI":"10.3934\/ipi.2013.7.397","volume":"7","author":"JM Bardsley","year":"2013","unstructured":"Bardsley, J.M.: Gaussian Markov random field priors for inverse problems. Inverse Problems and Imaging 7(2), 397\u2013416 (2013)","journal-title":"Inverse Problems and Imaging"},{"issue":"10\u201311","key":"10890_CR4","doi-asserted-by":"publisher","first-page":"1145","DOI":"10.1080\/00036810802140673","volume":"87","author":"L Baudouin","year":"2008","unstructured":"Baudouin, L., Mercado, A.: An inverse problem for Schr\u00f6dinger equations with discontinuous main coefficient. Appl. Anal. 87(10\u201311), 1145\u20131165 (2008)","journal-title":"Appl. Anal."},{"key":"10890_CR5","doi-asserted-by":"publisher","first-page":"1537","DOI":"10.1088\/0266-5611\/18\/6\/307","volume":"18","author":"L Baudouin","year":"2002","unstructured":"Baudouin, L., Puel, J.: Uniqueness and stability in an inverse problem for the Schr\u00f6dinger equation. Inverse Prob. 18, 1537\u20131554 (2002)","journal-title":"Inverse Prob."},{"key":"10890_CR6","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/j.jcp.2016.12.041","volume":"335","author":"A Beskos","year":"2017","unstructured":"Beskos, A., Girolami, M., Lan, S., Farrell, P., Stuart, A.: Geometric MCMC for infinite-dimensional inverse problems. J. Comput. Phys. 335, 327\u2013351 (2017)","journal-title":"J. Comput. Phys."},{"key":"10890_CR7","doi-asserted-by":"crossref","unstructured":"Bogachev, V.I.: Gaussian Measures. Mathematical Surveys and Monographs, vol. 62. American Mathematical Society, Rhode Island (1998)","DOI":"10.1090\/surv\/062"},{"key":"10890_CR8","doi-asserted-by":"crossref","unstructured":"Bui-Thanh, T., Ghattas, O.: An analysis of infinite dimensional Bayesian inverse shape acoustic scattering and its numerical approximation. SIAM\/ASA Journal on Uncertainty Quantification 2(1) (2014)","DOI":"10.1137\/120894877"},{"issue":"105001","key":"10890_CR9","first-page":"29","volume":"36","author":"A Carpio","year":"2020","unstructured":"Carpio, A., Iakunin, S., Stadler, G.: Bayesian approach to inverse scattering with topological priors. Inverse Prob. 36(105001), 29 (2020)","journal-title":"Inverse Prob."},{"issue":"075007","key":"10890_CR10","first-page":"28","volume":"39","author":"A Carpio","year":"2023","unstructured":"Carpio, A., Cebrian, E., Gutierrez, A.: Object based Bayesian full-waveform inversion for shear elastography. Inverse Prob. 39(075007), 28 (2023)","journal-title":"Inverse Prob."},{"issue":"1","key":"10890_CR11","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/s10711-013-9937-z","volume":"173","author":"F Chazal","year":"2014","unstructured":"Chazal, F., Silva, V.D., Oudot, S.: Persistence stability for geometric complexes. Geom. Dedicata. 173(1), 193\u2013214 (2014)","journal-title":"Geom. Dedicata."},{"issue":"10","key":"10890_CR12","doi-asserted-by":"publisher","first-page":"1251","DOI":"10.5802\/crmath.262","volume":"359","author":"M Choulli","year":"2021","unstructured":"Choulli, M.: Some stability inequalities for hybrid inverse problems. Comptes Rendus. Math\u00e9matique 359(10), 1251\u20131265 (2021)","journal-title":"Comptes Rendus. Math\u00e9matique"},{"issue":"4","key":"10890_CR13","doi-asserted-by":"publisher","first-page":"795","DOI":"10.1198\/106186005X76983","volume":"14","author":"J Christen","year":"2005","unstructured":"Christen, J., Fox, C.: Markov chain monte carlo using an approximation. J. Comput. Graph. Stat. 14(4), 795\u2013810 (2005)","journal-title":"J. Comput. Graph. Stat."},{"key":"10890_CR14","doi-asserted-by":"crossref","unstructured":"Cohen-Steiner, D., Edelsbrunner, H., Harer, J.: Stability of persistence diagrams. SCG \u201905: Proceedings of the twenty-first annual symposium on Computational geometry, 263\u2013271 (2005)","DOI":"10.1145\/1064092.1064133"},{"issue":"3","key":"10890_CR15","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1214\/13-STS421","volume":"28","author":"SL Cotter","year":"2013","unstructured":"Cotter, S.L., Roberts, G.O., Stuart, A.M., White, D.: MCMC methods for functions: modifying old algorithms to make them faster. Stat. Sci. 28(3), 424\u2013446 (2013)","journal-title":"Stat. Sci."},{"key":"10890_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-12385-1_7","volume-title":"The Bayesian Approach to Inverse Problems","author":"M Dashti","year":"2017","unstructured":"Dashti, M., Stuart, A.: The Bayesian Approach to Inverse Problems. Springer, Cham (2017)"},{"key":"10890_CR17","doi-asserted-by":"crossref","unstructured":"Edelsbrunner, H.: A Short Course in Computational Geometry and Topology. Springer Briefs in Applied Sciences and Technology $$\\cdot $$ Mathematical Methods. Springer, Cham Heidelberg (2014)","DOI":"10.1007\/978-3-319-05957-0"},{"key":"10890_CR18","doi-asserted-by":"crossref","unstructured":"Edelsbrunner, H., Harer, J.L.: Computational Topology: An Introduction. Student Mathematical Library (Volume 69). American Mathematical Society, Providence, Rhode Island (2010)","DOI":"10.1090\/mbk\/069"},{"issue":"055001","key":"10890_CR19","first-page":"24","volume":"40","author":"T Furuya","year":"2024","unstructured":"Furuya, T., Kow, P., Wang, J.: Consistency of the Bayes method for the inverse scattering problem. Inverse Prob. 40(055001), 24 (2024)","journal-title":"Inverse Prob."},{"issue":"085001","key":"10890_CR20","first-page":"35","volume":"36","author":"M Giordano","year":"2020","unstructured":"Giordano, M., Nickl, R.: Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem. Inverse Prob. 36(085001), 35 (2020)","journal-title":"Inverse Prob."},{"key":"10890_CR21","doi-asserted-by":"publisher","first-page":"1039","DOI":"10.1007\/s11222-014-9469-x","volume":"25","author":"A Golightly","year":"2015","unstructured":"Golightly, A., Henderson, D.A., Sherlock, C.: Delayed acceptance particle mcmc for exact inference in stochastic kinetic models. Statistics and Computation 25, 1039\u20131055 (2015)","journal-title":"Statistics and Computation"},{"issue":"5","key":"10890_CR22","doi-asserted-by":"publisher","first-page":"1077","DOI":"10.3934\/ipi.2021029","volume":"15","author":"J Huang","year":"2021","unstructured":"Huang, J., Deng, Z., Xu, L.: A Bayesian level set method for an inverse medium scattering problem in acoustics. Inverse Problems and Imaging 15(5), 1077\u20131097 (2021)","journal-title":"Inverse Problems and Imaging"},{"issue":"114001","key":"10890_CR23","first-page":"39","volume":"30","author":"MA Iglesias","year":"2014","unstructured":"Iglesias, M.A., Lin, K., Stuart, A.M.: Well-posed Bayesian geometric inverse problems arising in subsurface flow. Inverse Prob. 30(114001), 39 (2014)","journal-title":"Inverse Prob."},{"key":"10890_CR24","doi-asserted-by":"publisher","first-page":"181","DOI":"10.4171\/ifb\/362","volume":"18","author":"MA Iglesias","year":"2016","unstructured":"Iglesias, M.A., Lu, Y., Stuart, A.M.: A Bayesian level set method for geometric inverse problems. Interface and Free Boundaries 18, 181\u2013217 (2016)","journal-title":"Interface and Free Boundaries"},{"issue":"015008","key":"10890_CR25","first-page":"26","volume":"39","author":"B Jin","year":"2023","unstructured":"Jin, B., Lu, X., Quan, Q., Zhou, Z.: Convergence rate analysis of Galerkin approximation of inverse potential problem. Inverse Prob. 39(015008), 26 (2023)","journal-title":"Inverse Prob."},{"key":"10890_CR26","unstructured":"Jin, B., Quan, Q., Zhang, W.: Stochastic convergence analysis of inverse potential problem. https:\/\/arxiv.org\/html\/2410.14106v2 (2025)"},{"key":"10890_CR27","doi-asserted-by":"publisher","DOI":"10.1007\/b97315","volume-title":"Computational Homology","author":"T Kaczynski","year":"2004","unstructured":"Kaczynski, T., Mischaikow, K., Mrozek, M.: Computational Homology. Applied Mathematics Sciences. Springer, New York (2004)"},{"key":"10890_CR28","doi-asserted-by":"crossref","unstructured":"Kaipio, J.P., Somersalo, E.: Statistical and Computational Inverse Problems. Applied Mathematics Sciences, vol. 29. Springer, New York (2005)","DOI":"10.1007\/b138659"},{"issue":"084001","key":"10890_CR29","first-page":"19","volume":"35","author":"JP Kaipio","year":"2019","unstructured":"Kaipio, J.P., Huttunen, T., Luostari, T., L\u00e4hivaara, T., Monk, P.B.: A Bayesian approach to improving the Born approximation for inverse scattering with high-contrast materials. Inverse Prob. 35(084001), 19 (2019)","journal-title":"Inverse Prob."},{"key":"10890_CR30","doi-asserted-by":"crossref","unstructured":"Laghrib, A., Afraites, L., Nachaoui, M. (eds.): New Trends of Mathematical Inverse Problems and Applications, vol. 428. Springer, B\u00e9ni Mellal, Morocco (2022). ICNTAM 2022","DOI":"10.1007\/978-3-031-33069-8"},{"key":"10890_CR31","doi-asserted-by":"publisher","first-page":"1537","DOI":"10.1088\/0266-5611\/20\/5\/013","volume":"20","author":"M Lassas","year":"2004","unstructured":"Lassas, M., Siltanen, S.: Can one use total variation prior for edge-preserving bayesian inversion. Inverse Prob. 20, 1537\u20131563 (2004)","journal-title":"Inverse Prob."},{"issue":"1","key":"10890_CR32","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1137\/19M1270501","volume":"13","author":"Z Li","year":"2020","unstructured":"Li, Z., Deng, Z., Sun, J.: Extended-sampling-Bayesian method for limited aperture inverse scattering problems. SIAM J. Imag. Sci. 13(1), 422\u2013444 (2020)","journal-title":"SIAM J. Imag. Sci."},{"key":"10890_CR33","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1111\/j.1467-9868.2011.00777.x","volume":"73","author":"F Lindgren","year":"2011","unstructured":"Lindgren, F., Rue, H., Lindstr\u00f6m, J.: An explicit link between gaussian fields and gaussian markov random fields: the stochastic partial differential equation approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73, 423\u2013498 (2011)","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"issue":"2","key":"10890_CR34","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1515\/jiip-2017-0048","volume":"27","author":"M Markkanen","year":"2019","unstructured":"Markkanen, M., Roininen, L., Huttunen, J.M.J., Lasanen, S.: Cauchy difference priors for edge-preserving bayesian inversion. Journal of Inverse and Ill-posed Problems 27(2), 225\u2013240 (2019)","journal-title":"Journal of Inverse and Ill-posed Problems"},{"key":"10890_CR35","unstructured":"Miller, H.: Lectures on Algebraic Topology. World Scientific Publishing Co. Pte. Ltd., New Jersey (2022)"},{"issue":"8","key":"10890_CR36","doi-asserted-by":"publisher","first-page":"2697","DOI":"10.4171\/jems\/975","volume":"22","author":"R Nickl","year":"2020","unstructured":"Nickl, R.: Bernstein-von Mises theorems for statistical inverse problems I: Schr\u00f6dinger equation. J. Eur. Math. Soc. 22(8), 2697\u20132750 (2020)","journal-title":"J. Eur. Math. Soc."},{"issue":"1","key":"10890_CR37","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1137\/18M1236137","volume":"8","author":"R Nickl","year":"2020","unstructured":"Nickl, R., Geer, S., Wang, S.: Convergence rates for penalized least squares estimators in PDE constrained regression problems. SIAM Journal on Uncertainty Quantification 8(1), 374\u2013413 (2020)","journal-title":"SIAM Journal on Uncertainty Quantification"},{"key":"10890_CR38","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1152\/jappl.1948.1.2.93","volume":"1","author":"HH Pennes","year":"1948","unstructured":"Pennes, H.H.: Analysis of tissue and arterial blood temperatures in the resting human forearm. J. Appl. Physiol. 1, 93\u2013122 (1948)","journal-title":"J. Appl. Physiol."},{"key":"10890_CR39","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1017\/S0962492910000061","volume":"19","author":"AM Stuart","year":"2010","unstructured":"Stuart, A.M.: Inverse problems: A Bayesian perspective. Acta Numer 19, 451\u2013559 (2010)","journal-title":"Acta Numer"},{"key":"10890_CR40","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717921","volume-title":"Inverse Problem Theory and Methods for Model Parameter Estimation","author":"J Tarantola","year":"2005","unstructured":"Tarantola, J.: Inverse Problem Theory and Methods for Model Parameter Estimation. SIAM, Philadelphia (2005)"},{"key":"10890_CR41","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/s10665-009-9319-6","volume":"67","author":"D Trucu","year":"2010","unstructured":"Trucu, D., Ingham, D.B., Lesnic, D.: Space-dependent perfusion coefficient identification in the transient bio-heat equation. J. Engrg. Math. 67, 307\u2013315 (2010)","journal-title":"J. Engrg. Math."},{"key":"10890_CR42","doi-asserted-by":"crossref","unstructured":"Wang, Z., Bardsley, J.M., Solonen, A., Cui, T., Marzouk, Y.M.: Bayesian inverse problems with $$l_1$$ priors: A randomize-then-optimize approach. SIAM Journal on Scientific Computing 39(5) (2017)","DOI":"10.1137\/16M1080938"},{"key":"10890_CR43","doi-asserted-by":"publisher","first-page":"1181","DOI":"10.1088\/0266-5611\/17\/4\/340","volume":"17","author":"M Yamamoto","year":"2001","unstructured":"Yamamoto, M., Zou, J.: Simultaneous reconstruction of the initial temperature and heat radiative coefficitent. Inverse Prob. 17, 1181\u20131202 (2001)","journal-title":"Inverse Prob."},{"issue":"7","key":"10890_CR44","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/32\/7\/075006","volume":"32","author":"Z Yao","year":"2016","unstructured":"Yao, Z., Hu, Z., Li, J.: A TV-Gaussian prior for infinite-dimensional Bayesian inverse problems and its numerical implementations. Inverse Prob. 32(7), 075006 (2016)","journal-title":"Inverse Prob."},{"key":"10890_CR45","unstructured":"Zheng, Y.: Application of persistent homology in signal and image denoising. PhD thesis, Georg-August-Universit\u00e4t G\u00f6ttingen (2015)"},{"key":"10890_CR46","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546945","volume-title":"Topology for Computing","author":"AJ Zomorodian","year":"2005","unstructured":"Zomorodian, A.J.: Topology for Computing. Cambridge University Press, The Edinburgh Building, Cambridge, United Kindom (2005)"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-026-10890-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-026-10890-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-026-10890-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,23]],"date-time":"2026-05-23T12:52:04Z","timestamp":1779540724000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-026-10890-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,23]]},"references-count":46,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,8]]}},"alternative-id":["10890"],"URL":"https:\/\/doi.org\/10.1007\/s11222-026-10890-0","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,23]]},"assertion":[{"value":"10 September 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 April 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 May 2026","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"}}],"article-number":"147"}}