{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:27:40Z","timestamp":1772119660908,"version":"3.50.1"},"reference-count":62,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T00:00:00Z","timestamp":1723507200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T00:00:00Z","timestamp":1723507200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100005192","name":"Technical University of Denmark","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100005192","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>This work describes a Bayesian framework for reconstructing the boundaries that represent targeted features in an image, as well as the regularity (i.e., roughness vs. smoothness) of these boundaries. This regularity often carries crucial information in many inverse problem applications, e.g., for identifying malignant tissues in medical imaging. We represent the boundary as a radial function and characterize the regularity of this function by means of its fractional differentiability. We propose a hierarchical Bayesian formulation which, simultaneously, estimates the function and its regularity, and in addition we quantify the uncertainties in the estimates. Numerical results suggest that the proposed method is a reliable approach for estimating and characterizing object boundaries in imaging applications, as illustrated with examples from high-intensity X-ray CT and image inpainting with Gaussian and Laplace additive noise models. We also show that our method can quantify uncertainties for these noise types, various noise levels, and incomplete data scenarios.<\/jats:p>","DOI":"10.1007\/s10851-024-01207-9","type":"journal-article","created":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T09:03:13Z","timestamp":1723539793000},"page":"977-992","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Inferring Object Boundaries and Their Roughness with Uncertainty Quantification"],"prefix":"10.1007","volume":"66","author":[{"given":"Babak","family":"Maboudi Afkham","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicolai Andr\u00e9 Brogaard","family":"Riis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiqiu","family":"Dong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Per Christian","family":"Hansen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,8,13]]},"reference":[{"key":"1207_CR1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611976670","volume-title":"Computed Tomography: Algorithms, Insight, and Just Enough Theory","year":"2021","unstructured":"Hansen, P.C., J\u00f8rgensen, J.S., Lionheart, W.R.B. (eds.): Computed Tomography: Algorithms, Insight, and Just Enough Theory. SIAM, Philadelphia (2021). https:\/\/doi.org\/10.1137\/1.9781611976670"},{"key":"1207_CR2","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/27\/6\/065010","volume":"27","author":"AK Louis","year":"2011","unstructured":"Louis, A.K.: Feature reconstruction in inverse problems. Inverse Prob. 27, 065010 (2011)","journal-title":"Inverse Prob."},{"key":"1207_CR3","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1016\/j.jcp.2006.06.041","volume":"221","author":"R Ramlau","year":"2007","unstructured":"Ramlau, R., Ring, W.: A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data. J. Comput. Phys. 221, 539\u2013557 (2007)","journal-title":"J. Comput. Phys."},{"key":"1207_CR4","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6501\/aa950e","volume":"29","author":"VA Dahl","year":"2017","unstructured":"Dahl, V.A., Dahl, A.B., Hansen, P.C.: Computing segmentations directly from X-ray projection data via parametric deformable curves. Meas. Sci. Technol. 29, 014003 (2017)","journal-title":"Meas. Sci. Technol."},{"key":"1207_CR5","doi-asserted-by":"crossref","unstructured":"Batenburg, K.J., Sijbers, J.: Dart: a fast heuristic algebraic reconstruction algorithm for discrete tomography. In: 2007 IEEE International Conference on Image Processing, vol. 4, p. 133. IEEE (2007)","DOI":"10.1109\/ICIP.2007.4379972"},{"issue":"9","key":"1207_CR6","doi-asserted-by":"publisher","first-page":"2542","DOI":"10.1109\/TIP.2011.2131661","volume":"20","author":"KJ Batenburg","year":"2011","unstructured":"Batenburg, K.J., Sijbers, J.: DART: a practical reconstruction algorithm for discrete tomography. IEEE Trans. Image Process. 20(9), 2542\u20132553 (2011)","journal-title":"IEEE Trans. Image Process."},{"issue":"8","key":"1207_CR7","doi-asserted-by":"publisher","first-page":"2146","DOI":"10.1109\/TIP.2011.2114894","volume":"20","author":"FJ Maestre-Deusto","year":"2011","unstructured":"Maestre-Deusto, F.J., Scavello, G., Pizarro, J., Galindo, P.L.: Adart: an adaptive algebraic reconstruction algorithm for discrete tomography. IEEE Trans. Image Process. 20(8), 2146\u20132152 (2011)","journal-title":"IEEE Trans. Image Process."},{"issue":"1","key":"1207_CR8","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1109\/TIP.2015.2504869","volume":"25","author":"X Zhuge","year":"2015","unstructured":"Zhuge, X., Palenstijn, W.J., Batenburg, K.J.: TVR-DART: a more robust algorithm for discrete tomography from limited projection data with automated gray value estimation. IEEE Trans. Image Process. 25(1), 455\u2013468 (2015)","journal-title":"IEEE Trans. Image Process."},{"key":"1207_CR9","doi-asserted-by":"crossref","unstructured":"Kadu, A., Leeuwen, T., Batenburg, K.J.: A parametric level-set method for partially discrete tomography. In: Discrete Geometry for Computer Imagery: 20th IAPR International Conference, DGCI 2017, Vienna, Austria, September 19\u201321, 2017, Proceedings 20, pp. 122\u2013134. Springer (2017)","DOI":"10.1007\/978-3-319-66272-5_11"},{"issue":"2","key":"1207_CR10","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1109\/TMI.2017.2756078","volume":"37","author":"D Liu","year":"2017","unstructured":"Liu, D., Khambampati, A.K., Du, J.: A parametric level set method for electrical impedance tomography. IEEE Trans. Med. Imaging 37(2), 451\u2013460 (2017)","journal-title":"IEEE Trans. Med. Imaging"},{"issue":"2","key":"1207_CR11","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1016\/j.jcp.2006.06.041","volume":"221","author":"R Ramlau","year":"2007","unstructured":"Ramlau, R., Ring, W.: A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data. J. Comput. Phys. 221(2), 539\u2013557 (2007)","journal-title":"J. Comput. Phys."},{"issue":"6","key":"1207_CR12","doi-asserted-by":"publisher","first-page":"1555","DOI":"10.1007\/s11222-016-9704-8","volume":"27","author":"MM Dunlop","year":"2016","unstructured":"Dunlop, M.M., Iglesias, M.A., Stuart, A.M.: Hierarchical Bayesian level set inversion. Stat. Comput. 27(6), 1555\u20131584 (2016). https:\/\/doi.org\/10.1007\/s11222-016-9704-8","journal-title":"Stat. Comput."},{"issue":"2","key":"1207_CR13","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. Interfaces Free Bound. 18(2), 181\u2013217 (2016)","journal-title":"Interfaces Free Bound."},{"issue":"1","key":"1207_CR14","doi-asserted-by":"publisher","first-page":"4329","DOI":"10.1038\/s41598-019-40437-5","volume":"9","author":"EJ Limkin","year":"2019","unstructured":"Limkin, E.J., Reuz\u00e9, S., Carr\u00e9, A., Sun, R., Schernberg, A., Alexis, A., Deutsch, E., Fert\u00e9, C., Robert, C.: The complexity of tumor shape, spiculatedness, correlates with tumor radiomic shape features. Sci. Rep. 9(1), 4329 (2019)","journal-title":"Sci. Rep."},{"issue":"3","key":"1207_CR15","doi-asserted-by":"publisher","first-page":"455","DOI":"10.3171\/jns.1999.90.3.0455","volume":"90","author":"S Nakasu","year":"1999","unstructured":"Nakasu, S., Nakasu, Y., Nakajima, M., Matsuda, M., Handa, J.: Preoperative identification of meningiomas that are highly likely to recur. J. Neurosurg. 90(3), 455\u2013462 (1999)","journal-title":"J. Neurosurg."},{"key":"1207_CR16","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1016\/j.suronc.2019.05.005","volume":"29","author":"P Sanghani","year":"2019","unstructured":"Sanghani, P., Ti, A.B., King, N.K.K., Ren, H.: Evaluation of tumor shape features for overall survival prognosis in glioblastoma multiforme patients. Surg. Oncol. 29, 178\u2013183 (2019)","journal-title":"Surg. Oncol."},{"issue":"1","key":"1207_CR17","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1093\/icvts\/ivs055","volume":"15","author":"T Baba","year":"2012","unstructured":"Baba, T., Uramoto, H., Takenaka, M., Oka, S., Shigematsu, Y., Shimokawa, H., Hanagiri, T., Tanaka, F.: The tumour shape of lung adenocarcinoma is related to the postoperative prognosis. Interact. Cardiovasc. Thorac. Surg. 15(1), 73\u201376 (2012)","journal-title":"Interact. Cardiovasc. Thorac. Surg."},{"issue":"5","key":"1207_CR18","doi-asserted-by":"publisher","first-page":"717","DOI":"10.7150\/jca.82592","volume":"14","author":"X-X Yin","year":"2023","unstructured":"Yin, X.-X., Jian, Y., Shen, J., Wu, J., Zhang, Y., Wang, W.: Focal boundary dice: improved breast tumor segmentation from MRI scan. J. Cancer 14(5), 717 (2023)","journal-title":"J. Cancer"},{"issue":"1","key":"1207_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1029\/RG023i001p00001","volume":"23","author":"CG Fox","year":"1985","unstructured":"Fox, C.G., Hayes, D.E.: Quantitative methods for analyzing the roughness of the seafloor. Rev. Geophys. 23(1), 1\u201348 (1985)","journal-title":"Rev. Geophys."},{"issue":"5","key":"1207_CR20","doi-asserted-by":"publisher","first-page":"2190","DOI":"10.1214\/16-AOS1523","volume":"45","author":"M Li","year":"2017","unstructured":"Li, M., Ghosal, S.: Bayesian detection of image boundaries. Ann. Stat. 45(5), 2190\u20132217 (2017). https:\/\/doi.org\/10.1214\/16-AOS1523","journal-title":"Ann. Stat."},{"issue":"2","key":"1207_CR21","doi-asserted-by":"publisher","first-page":"149","DOI":"10.32614\/RJ-2017-052","volume":"9","author":"N Syring","year":"2017","unstructured":"Syring, N., Li, M.: BayesBD: an R package for Bayesian inference on image boundaries. R J. 9(2), 149\u2013162 (2017). https:\/\/doi.org\/10.32614\/RJ-2017-052","journal-title":"R J."},{"key":"1207_CR22","first-page":"1","volume-title":"An Introduction to Fractional Calculus","author":"PL Butzer","year":"2000","unstructured":"Butzer, P.L., Westphal, U.: An Introduction to Fractional Calculus, pp. 1\u201385. World Scientific, Singapore (2000)"},{"key":"1207_CR23","doi-asserted-by":"publisher","DOI":"10.1142\/3779","volume-title":"Applications of Fractional Calculus in Physics","author":"R Hilfer","year":"2000","unstructured":"Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)"},{"key":"1207_CR24","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1016\/j.cnsns.2018.04.019","volume":"64","author":"H Sun","year":"2018","unstructured":"Sun, H., Zhang, Y., Baleanu, D., Chen, W., Chen, Y.: A new collection of real world applications of fractional calculus in science and engineering. Commun. Nonlinear Sci. Numer. Simul. 64, 213\u2013231 (2018)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"1207_CR25","doi-asserted-by":"crossref","unstructured":"Afkham, B.M., Dong, Y., Hansen, P.C.: Uncertainty quantification of inclusion boundaries in the context of X-ray tomography. SIAM\/ASA J. Uncertain. Quant. (2022) (to appear)","DOI":"10.1137\/21M1433782"},{"key":"1207_CR26","volume-title":"Statistical and Computational Inverse Problems","author":"J Kaipio","year":"2006","unstructured":"Kaipio, J., Somersalo, E.: Statistical and Computational Inverse Problems. Springer, Berlin (2006)"},{"issue":"4","key":"1207_CR27","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.3934\/ipi.2016030","volume":"10","author":"MM Dunlop","year":"2016","unstructured":"Dunlop, M.M., Stuart, A.M.: The Bayesian formulation of EIT: analysis and algorithms. Inverse Probl. Imaging 10(4), 1007\u20131036 (2016). https:\/\/doi.org\/10.3934\/ipi.2016030","journal-title":"Inverse Probl. Imaging"},{"key":"1207_CR28","doi-asserted-by":"publisher","first-page":"4","DOI":"10.4171\/mag\/99","volume":"125","author":"A Carpio","year":"2022","unstructured":"Carpio, A.: Seeing the invisible: digital holography. Eur. Math. Soc. Mag. 125, 4\u201312 (2022)","journal-title":"Eur. Math. Soc. Mag."},{"issue":"8","key":"1207_CR29","doi-asserted-by":"publisher","first-page":"2020","DOI":"10.1029\/2020WR027110","volume":"56","author":"T Xu","year":"2020","unstructured":"Xu, T., Reuschen, S., Nowak, W., Hendricks Franssen, H.-J.: Preconditioned Crank-Nicolson Markov chain Monte Carlo coupled with parallel tempering: An efficient method for Bayesian inversion of multi-Gaussian log-hydraulic conductivity fields. Water Resour. Res. 56(8), 2020\u2013027110 (2020)","journal-title":"Water Resour. Res."},{"issue":"10","key":"1207_CR30","doi-asserted-by":"publisher","first-page":"2020","DOI":"10.1029\/2020WR027391","volume":"56","author":"A Alghamdi","year":"2020","unstructured":"Alghamdi, A., Hesse, M.A., Chen, J., Ghattas, O.: Bayesian poroelastic aquifer characterization from InSAR surface deformation data. part I: maximum a posteriori estimate. Water Resour. Res. 56(10), 2020\u2013027391 (2020)","journal-title":"Water Resour. Res."},{"issue":"11","key":"1207_CR31","doi-asserted-by":"publisher","first-page":"2021","DOI":"10.1029\/2021WR029775","volume":"57","author":"A Alghamdi","year":"2021","unstructured":"Alghamdi, A., Hesse, M.A., Chen, J., Villa, U., Ghattas, O.: Bayesian poroelastic aquifer characterization from InSAR surface deformation data. 2. Quantifying the uncertainty. Water Resour. Res. 57(11), 2021\u2013029775 (2021)","journal-title":"Water Resour. Res."},{"key":"1207_CR32","unstructured":"Orozco, R., Louboutin, M., Siahkoohi, A., Rizzuti, G., Leeuwen, T., Herrmann, F.: Amortized normalizing flows for transcranial ultrasound with uncertainty quantification. arXiv preprint arXiv:2303.03478 (2023)"},{"issue":"7","key":"1207_CR33","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1016\/j.compmedimag.2008.12.007","volume":"33","author":"Y Chen","year":"2009","unstructured":"Chen, Y., Gao, D., Nie, C., Luo, L., Chen, W., Yin, X., Lin, Y.: Bayesian statistical reconstruction for low-dose X-ray computed tomography using an adaptive-weighting nonlocal prior. Comput. Med. Imaging Graph. 33(7), 495\u2013500 (2009)","journal-title":"Comput. Med. Imaging Graph."},{"issue":"4","key":"1207_CR34","doi-asserted-by":"publisher","first-page":"1951","DOI":"10.1121\/1.4945990","volume":"139","author":"J Tick","year":"2016","unstructured":"Tick, J., Pulkkinen, A., Tarvainen, T.: Image reconstruction with uncertainty quantification in photoacoustic tomography. J. Acoust. Soc. Am. 139(4), 1951\u20131961 (2016)","journal-title":"J. Acoust. Soc. Am."},{"issue":"3","key":"1207_CR35","doi-asserted-by":"publisher","first-page":"1523","DOI":"10.1093\/gji\/ggab287","volume":"227","author":"M Izzatullah","year":"2021","unstructured":"Izzatullah, M., Van Leeuwen, T., Peter, D.: Bayesian seismic inversion: a fast sampling Langevin dynamics Markov chain Monte Carlo method. Geophys. J. Int. 227(3), 1523\u20131553 (2021)","journal-title":"Geophys. J. Int."},{"issue":"6","key":"1207_CR36","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6501\/ac5437","volume":"33","author":"JP Molnar","year":"2022","unstructured":"Molnar, J.P., Grauer, S.J.: Flow field tomography with uncertainty quantification using a Bayesian physics-informed neural network. Meas. Sci. Technol. 33(6), 065305 (2022)","journal-title":"Meas. Sci. Technol."},{"issue":"5","key":"1207_CR37","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1016\/j.bulsci.2011.12.004","volume":"136","author":"E Di Nezza","year":"2012","unstructured":"Di Nezza, E., Palatucci, G., Valdinoci, E.: Hitchhiker\u2019s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136(5), 521\u2013573 (2012). https:\/\/doi.org\/10.1016\/j.bulsci.2011.12.004","journal-title":"Bull. Sci. Math."},{"issue":"2","key":"1207_CR38","doi-asserted-by":"publisher","first-page":"561","DOI":"10.3934\/ipi.2014.8.561","volume":"8","author":"L Roininen","year":"2014","unstructured":"Roininen, L., Huttunen, J.M.J., Lasanen, S.: Whittle\u2013Mat\u00e9rn priors for Bayesian statistical inversion with applications in electrical impedance tomography. Inverse Probl. Imaging 8(2), 561\u2013586 (2014)","journal-title":"Inverse Probl. Imaging"},{"key":"1207_CR39","unstructured":"Owen, A.B.: Monte Carlo Theory, Methods and Examples (Book in progress) (2013). https:\/\/artowen.su.domains\/mc\/"},{"key":"1207_CR40","volume-title":"Gaussian Random Processes","author":"IA Ibragimov","year":"2012","unstructured":"Ibragimov, I.A., Rozanov, Y.A.: Gaussian Random Processes. Springer, Berlin (2012)"},{"key":"1207_CR41","doi-asserted-by":"publisher","DOI":"10.1142\/12237","volume-title":"The Multivariate Normal Distribution: Theory and Applications","author":"T Pham-Gia","year":"2021","unstructured":"Pham-Gia, T.: The Multivariate Normal Distribution: Theory and Applications. World Scientific, Singapore (2021)"},{"issue":"47","key":"1207_CR42","first-page":"1593","volume":"15","author":"MD Hoffman","year":"2014","unstructured":"Hoffman, M.D., Gelman, A.: The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J. Mach. Learn. Res. 15(47), 1593\u20131623 (2014)","journal-title":"J. Mach. Learn. Res."},{"key":"1207_CR43","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971514","author":"WL Briggs","year":"1995","unstructured":"Briggs, W.L., Henson, V.E.: The DFT: an owner\u2019s manual for the discrete Fourier transform. Soc. Ind. Appl. Math. (1995). https:\/\/doi.org\/10.1137\/1.9781611971514","journal-title":"Soc. Ind. Appl. Math."},{"key":"1207_CR44","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4374-8","volume-title":"Probability","author":"J Pitman","year":"1993","unstructured":"Pitman, J.: Probability. Springer, New York (1993)"},{"issue":"3","key":"1207_CR45","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1109\/51.677174","volume":"17","author":"N Radhakrishnan","year":"1998","unstructured":"Radhakrishnan, N., Gangadhar, B.N.: Estimating regularity in epileptic seizure time-series data. IEEE Eng. Med. Biol. Mag. 17(3), 89\u201394 (1998). https:\/\/doi.org\/10.1109\/51.677174","journal-title":"IEEE Eng. Med. Biol. Mag."},{"issue":"1","key":"1207_CR46","doi-asserted-by":"publisher","first-page":"23","DOI":"10.3233\/THC-181548","volume":"28","author":"Y Gao","year":"2020","unstructured":"Gao, Y., Zhao, Z., Chen, Y., Mahara, G., Huang, J., Lin, Z., Zhang, J.: Automatic epileptic seizure classification in multichannel EEG time series with linear discriminant analysis. Technol. Health Care 28(1), 23\u201333 (2020)","journal-title":"Technol. Health Care"},{"key":"1207_CR47","volume-title":"p-and hp-Finite Element Methods: Theory and Applications in Solid and Fluid Mechanics","author":"C Schwab","year":"1998","unstructured":"Schwab, C.: p-and hp-Finite Element Methods: Theory and Applications in Solid and Fluid Mechanics. Oxford University Press, Oxford (1998)"},{"key":"1207_CR48","doi-asserted-by":"crossref","unstructured":"Riis, N.A.B., Alghamdi, A.M.A., Uribe, F., Christensen, S.L., Afkham, B.M., Hansen, P.C., J\u00f8rgensen, J.S.: CUQIpy\u2014Part I: computational uncertainty quantification for inverse problems in Python. Inverse Probl. (2023) (submitted)","DOI":"10.1088\/1361-6420\/ad22e7"},{"key":"1207_CR49","unstructured":"CUQIpy software. GitHub (2023)"},{"key":"1207_CR50","unstructured":"Afkham, B.M., Riis, N.A.B.: Python codes for inferring objects with uncertain roughness. GitHub (2023). https:\/\/github.com\/babakmaboudi\/uncertain_roughness"},{"key":"1207_CR51","doi-asserted-by":"publisher","DOI":"10.1201\/9780429258411","volume-title":"Bayesian Data Analysis","author":"A Gelman","year":"1995","unstructured":"Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. Chapman and Hall\/CRC, Boca Raton (1995)"},{"issue":"1","key":"1207_CR52","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1006\/jmps.1999.1278","volume":"44","author":"L Wasserman","year":"2000","unstructured":"Wasserman, L.: Bayesian model selection and model averaging. J. Math. Psychol. 44(1), 92\u2013107 (2000)","journal-title":"J. Math. Psychol."},{"key":"1207_CR53","doi-asserted-by":"crossref","unstructured":"Chipman, H., George, E.I., McCulloch, R.E., Clyde, M., Foster, D.P., Stine, R.A.: The practical implementation of Bayesian model selection. Lecture Notes-Monograph Series, pp. 65\u2013134 (2001)","DOI":"10.1214\/lnms\/1215540964"},{"key":"1207_CR54","unstructured":"Minka, T.: Bayesian linear regression. Technical report (2000). https:\/\/tminka.github.io\/papers\/minka-linear.pdf"},{"issue":"3","key":"1207_CR55","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":"1207_CR56","doi-asserted-by":"publisher","unstructured":"Krishnan, V.P., Quinto, E.T.: In: Scherzer, O. (ed.) Microlocal Analysis in Tomography, pp. 847\u2013902. Springer, New York (2015). https:\/\/doi.org\/10.1007\/978-1-4939-0790-8_36","DOI":"10.1007\/978-1-4939-0790-8_36"},{"key":"1207_CR57","unstructured":"Weisstein, E.W.: Gear Curve. MathWorld. https:\/\/mathworld.wolfram.com\/GearCurve.html"},{"key":"1207_CR58","volume-title":"Digital Image Processing","author":"KR Castleman","year":"1996","unstructured":"Castleman, K.R.: Digital Image Processing. Prentice Hall Press, Hoboken (1996)"},{"key":"1207_CR59","doi-asserted-by":"publisher","unstructured":"Zhang, X.-Q., Froment, J.: Total variation based Fourier reconstruction and regularization for computer tomography. In: IEEE Nuclear Science Symposium Conference Record, 2005, vol. 4, pp. 2332\u20132336 (2005).https:\/\/doi.org\/10.1109\/NSSMIC.2005.1596801","DOI":"10.1109\/NSSMIC.2005.1596801"},{"key":"1207_CR60","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511734304","volume-title":"Partial Differential Equation Methods for Image Inpainting","author":"C-B Sch\u00f6nlieb","year":"2015","unstructured":"Sch\u00f6nlieb, C.-B.: Partial Differential Equation Methods for Image Inpainting. Cambridge University Press, Cambridge (2015)"},{"key":"1207_CR61","doi-asserted-by":"crossref","unstructured":"Chan, R.H., Dong, Y., Hinterm\u00fcller, M.: An efficient two-phase L1-TV method for restoring blurred image with impulse noise. IEEE Trans. Image Process. 19, 1731\u20131739 (2010)","DOI":"10.1109\/TIP.2010.2045148"},{"issue":"2","key":"1207_CR62","doi-asserted-by":"publisher","first-page":"183","DOI":"10.3934\/ipi.2012.6.183","volume":"6","author":"M Dashti","year":"2012","unstructured":"Dashti, M., Harris, S., Stuart, A.: Besov priors for Bayesian inverse problems. Inverse Probl. Imaging 6(2), 183\u2013200 (2012). https:\/\/doi.org\/10.3934\/ipi.2012.6.183","journal-title":"Inverse Probl. Imaging"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-024-01207-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10851-024-01207-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-024-01207-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,11]],"date-time":"2024-11-11T09:04:37Z","timestamp":1731315877000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10851-024-01207-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,13]]},"references-count":62,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["1207"],"URL":"https:\/\/doi.org\/10.1007\/s10851-024-01207-9","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-3894410\/v1","asserted-by":"object"}]},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,13]]},"assertion":[{"value":"24 January 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 July 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 August 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}