{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T07:11:04Z","timestamp":1774595464543,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2020,7,22]],"date-time":"2020-07-22T00:00:00Z","timestamp":1595376000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,7,22]],"date-time":"2020-07-22T00:00:00Z","timestamp":1595376000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"ETH Foundations of Data Science"},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["FOR 1548"],"award-info":[{"award-number":["FOR 1548"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008398","name":"Villum Fonden","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008398","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2021,1]]},"DOI":"10.1007\/s00454-020-00225-9","type":"journal-article","created":{"date-parts":[[2020,7,22]],"date-time":"2020-07-22T19:03:38Z","timestamp":1595444618000},"page":"1-42","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Reconstruction of Convex Bodies from Moments"],"prefix":"10.1007","volume":"65","author":[{"given":"Astrid","family":"Kousholt","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3501-7588","authenticated-orcid":false,"given":"Julia","family":"Schulte","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,7,22]]},"reference":[{"issue":"1","key":"225_CR1","doi-asserted-by":"publisher","first-page":"13","DOI":"10.4171\/ZAA\/866","volume":"18","author":"DD Ang","year":"1999","unstructured":"Ang, D.D., Gorenflo, R., Trong, D.D.: A multi-dimensional Hausdorff moment problem: regularization by finite moments. Z. Anal. Anwendungen 18(1), 13\u201325 (1999)","journal-title":"Z. Anal. Anwendungen"},{"issue":"4","key":"225_CR2","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1007\/s00365-001-0024-6","volume":"18","author":"T Bagby","year":"2002","unstructured":"Bagby, T., Bos, L., Levenberg, N.: Multivariate simultaneous approximation. Constr. Approx. 18(4), 569\u2013577 (2002)","journal-title":"Constr. Approx."},{"key":"225_CR3","doi-asserted-by":"crossref","unstructured":"Bhatia, R.: Matrix Analysis. Graduate Texts in Mathematics, vol. 169. Springer, New York (1997)","DOI":"10.1007\/978-1-4612-0653-8"},{"issue":"6","key":"225_CR4","doi-asserted-by":"publisher","first-page":"727","DOI":"10.1007\/s10958-008-9144-x","volume":"153","author":"EM Bronstein","year":"2008","unstructured":"Bronstein, E.M.: Approximation of convex sets by polytopes. J. Math. Sci. 153(6), 727\u2013762 (2008)","journal-title":"J. Math. Sci."},{"issue":"6","key":"225_CR5","doi-asserted-by":"publisher","first-page":"3118","DOI":"10.1016\/j.aim.2012.08.015","volume":"231","author":"S Campi","year":"2012","unstructured":"Campi, S., Gardner, R.J., Gronchi, P., Kiderlen, M.: Lightness functions. Adv. Math. 231(6), 3118\u20133146 (2012)","journal-title":"Adv. Math."},{"issue":"1","key":"225_CR6","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1006\/jfan.1994.1086","volume":"123","author":"MC Delfour","year":"1994","unstructured":"Delfour, M.C., Zol\u00e9sio, J.-P.: Shape analysis via oriented distance functions. J. Funct. Anal. 123(1), 129\u2013201 (1994)","journal-title":"J. Funct. Anal."},{"key":"225_CR7","doi-asserted-by":"crossref","unstructured":"Diaconis, P.: Application of the method of moments in probability and statistics. In: Moments in Mathematics (San Antonio 1987). Proceedings of Symposia in Applied Mathematics, vol. 37, pp. 125\u2013142. American Mathematical Society, Providence (1987)","DOI":"10.1090\/psapm\/037\/921087"},{"key":"225_CR8","unstructured":"Gardner, R.J.: Geometric Tomography. Encyclopedia of Mathematics and its Applications, vol. 58. Cambridge University Press, New York (2006)"},{"issue":"2","key":"225_CR9","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/s00454-002-0759-2","volume":"29","author":"RJ Gardner","year":"2003","unstructured":"Gardner, R.J., Milanfar, P.: Reconstruction of convex bodies from brightness functions. Discrete Comput. Geom. 29(2), 279\u2013303 (2003)","journal-title":"Discrete Comput. Geom."},{"key":"225_CR10","doi-asserted-by":"crossref","unstructured":"Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Classics in Mathematics. Springer, Berlin (2001)","DOI":"10.1007\/978-3-642-61798-0"},{"issue":"4","key":"225_CR11","doi-asserted-by":"publisher","first-page":"1222","DOI":"10.1137\/S1064827597328315","volume":"21","author":"GH Golub","year":"1999","unstructured":"Golub, G.H., Milanfar, P., Varah, J.: A stable numerical method for inverting shape from moments. SIAM J. Sci. Comput. 21(4), 1222\u20131243 (1999)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"225_CR12","doi-asserted-by":"publisher","first-page":"596","DOI":"10.1007\/s00454-012-9426-4","volume":"48","author":"N Gravin","year":"2012","unstructured":"Gravin, N., Lasserre, J., Pasechnik, D.V., Robins, S.: The inverse moment problem for convex polytopes. Discrete Comput. Geom. 48(3), 596\u2013621 (2012)","journal-title":"Discrete Comput. Geom."},{"issue":"4","key":"225_CR13","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1088\/0266-5611\/16\/4\/312","volume":"16","author":"B Gustafsson","year":"2000","unstructured":"Gustafsson, B., He, C., Milanfar, P., Putinar, M.: Reconstructing planar domains from their moments. Inverse Probl. 16(4), 1053\u20131070 (2000)","journal-title":"Inverse Probl."},{"key":"225_CR14","doi-asserted-by":"crossref","unstructured":"Johnson, C.R. (ed.): Matrix Theory and Applications (Phoenix 1989). Proceedings of Symposia in Applied Mathematics, vol. 40. American Mathematical Society, Providence (1990)","DOI":"10.1090\/psapm\/040"},{"key":"225_CR15","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.aam.2016.09.004","volume":"83","author":"A Kousholt","year":"2017","unstructured":"Kousholt, A.: Reconstruction of $$n$$-dimensional convex bodies from surface tensors. Adv. Appl. Math. 83, 115\u2013144 (2017)","journal-title":"Adv. Appl. Math."},{"key":"225_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.aam.2016.01.001","volume":"76","author":"A Kousholt","year":"2016","unstructured":"Kousholt, A., Kiderlen, M.: Reconstruction of convex bodies from surface tensors. Adv. Appl. Math. 76, 1\u201333 (2016)","journal-title":"Adv. Appl. Math."},{"key":"225_CR17","volume-title":"The Implicit Function Theorem: History, Theory, and Applications","author":"SG Krantz","year":"2002","unstructured":"Krantz, S.G., Parks, H.R.: The Implicit Function Theorem: History, Theory, and Applications. Birkh\u00e4user, Boston (2002)"},{"key":"225_CR18","unstructured":"Krein, M.G., Nudel\u2019man, A.A.: The Markov Moment Problem and Extremal Problems. Translations of Mathematical Monographs, vol. 50. American Mathematical Society, Providence (1977)"},{"issue":"3","key":"225_CR19","doi-asserted-by":"publisher","first-page":"796","DOI":"10.1137\/S1052623400366802","volume":"11","author":"JB Lasserre","year":"2001","unstructured":"Lasserre, J.B.: Global optimization with polynomials and the problem of moments. SIAM J. Optim. 11(3), 796\u2013817 (2001)","journal-title":"SIAM J. Optim."},{"issue":"10","key":"225_CR20","doi-asserted-by":"publisher","first-page":"1693","DOI":"10.1364\/JOSAA.9.001693","volume":"9","author":"AS Lele","year":"1992","unstructured":"Lele, A.S., Kulkarni, S.R., Willsky, A.S.: Convex-polygon estimation from support-line measurements and applications to target reconstruction from laser-radar data. J. Opt. Soc. Am. A 9(10), 1693\u20131714 (1992)","journal-title":"J. Opt. Soc. Am. A"},{"key":"225_CR21","doi-asserted-by":"publisher","DOI":"10.1142\/3848","volume-title":"Applied Functional Analysis and Partial Differential Equations","author":"M Miklav\u010di\u010d","year":"1998","unstructured":"Miklav\u010di\u010d, M.: Applied Functional Analysis and Partial Differential Equations. World Scientific, River Edge (1998)"},{"issue":"2","key":"225_CR22","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1109\/78.348126","volume":"43","author":"P Milanfar","year":"1995","unstructured":"Milanfar, P., Verghese, G.C., Karl, W.C., Willsky, A.S.: Reconstructing polygons from moments with connections to array processing. IEEE Trans. Image Process. 43(2), 432\u2013443 (1995)","journal-title":"IEEE Trans. Image Process."},{"issue":"3","key":"225_CR23","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1109\/83.491319","volume":"5","author":"P Milanfar","year":"1996","unstructured":"Milanfar, P., Karl, W.C., Willsky, A.S.: A moment-based variational approach to tomographic reconstruction. IEEE Trans. Image Process. 5(3), 459\u2013470 (1996)","journal-title":"IEEE Trans. Image Process."},{"key":"225_CR24","doi-asserted-by":"crossref","unstructured":"Paouris, G.: $$\\Psi _2$$-Estimates for linear functionals on zonoids. In: Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol. 1807, pp. 211\u2013222. Springer, Berlin (2003)","DOI":"10.1007\/978-3-540-36428-3_17"},{"key":"225_CR25","doi-asserted-by":"crossref","unstructured":"Pollard, D.: Convergence of Stochastic Processes. Springer Series in Statistics. Springer, New York (1984)","DOI":"10.1007\/978-1-4612-5254-2"},{"issue":"4","key":"225_CR26","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1109\/34.50623","volume":"12","author":"JL Prince","year":"1990","unstructured":"Prince, J.L., Willsky, A.S.: Reconstructing convex sets from support line measurements. IEEE Trans. Pattern Anal. Mach. Intell. 12(4), 377\u2013389 (1990)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"1","key":"225_CR27","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1006\/jath.1997.3117","volume":"92","author":"M Putinar","year":"1998","unstructured":"Putinar, M.: Extremal solutions of the two-dimensional $$L$$-problem of moments, II. J. Approx. Theory 92(1), 38\u201358 (1998)","journal-title":"J. Approx. Theory"},{"issue":"1","key":"225_CR28","first-page":"23","volume":"9","author":"S Rabinowitz","year":"1997","unstructured":"Rabinowitz, S.: A polynomial curve of constant width. Mo. J. Math. Sci. 9(1), 23\u201327 (1997)","journal-title":"Mo. J. Math. Sci."},{"key":"225_CR29","unstructured":"Schneider, R.: Convex Bodies: The Brunn\u2013Minkowski Theory. Encyclopedia of Mathematics and its Applications, vol. 151. Cambridge University Press, Cambridge (2014)"},{"issue":"1","key":"225_CR30","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1016\/0022-247X(87)90352-0","volume":"122","author":"MI Sezan","year":"1987","unstructured":"Sezan, M.I., Stark, H.: Incorporation of a priori moment information into signal recovery and synthesis problems. J. Math. Anal. Appl. 122(1), 172\u2013186 (1987)","journal-title":"J. Math. Anal. Appl."},{"key":"225_CR31","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1112\/S0025579300005179","volume":"12","author":"GC Shephard","year":"1965","unstructured":"Shephard, G.C., Webster, R.J.: Metrics for sets of convex bodies. Mathematika 12, 73\u201388 (1965)","journal-title":"Mathematika"},{"issue":"3","key":"225_CR32","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1088\/0266-5611\/3\/3\/016","volume":"3","author":"G Talenti","year":"1987","unstructured":"Talenti, G.: Recovering a function from a finite number of moments. Inverse Probl. 3(3), 501\u2013517 (1987)","journal-title":"Inverse Probl."},{"key":"225_CR33","unstructured":"Taussky, O. (ed.): Contributions to the Solution of Systems of Linear Equations and the Determination of Eigenvalues. Applied Mathematics Series, vol. 39. US National Bureau of Standards (1954)"},{"key":"225_CR34","doi-asserted-by":"crossref","unstructured":"Waki, H., Kim, S., Kojima, M., Muramatsu, M., Sugimoto, H.: Algorithm 883: sparsePOP\u2013a sparse semidefinite programming relaxation of polynomial optimization problems. ACM Trans. Math. Softw. 35(2), #\u00a015 (2009)","DOI":"10.1145\/1377612.1377619"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00225-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-020-00225-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-020-00225-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,21]],"date-time":"2021-07-21T23:49:16Z","timestamp":1626911356000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-020-00225-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,22]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["225"],"URL":"https:\/\/doi.org\/10.1007\/s00454-020-00225-9","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,22]]},"assertion":[{"value":"23 May 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 April 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 July 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}