{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T01:54:04Z","timestamp":1790474044733,"version":"4.1.0"},"reference-count":42,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"name":"Euclid Collaboration"},{"DOI":"10.13039\/501100002830","name":"Centre National d'Etudes Spatiales","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002830","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["640174"],"award-info":[{"award-number":["640174"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["665044"],"award-info":[{"award-number":["665044"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000844","name":"European Space Agency","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000844","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>In astronomy, observing large fractions of the sky within a reasonable amount of time implies using large field-of-view optical instruments that typically have a spatially varying point spread function (PSF). Depending on the scientific goals, galaxy images need to be corrected for the PSF, whereas no direct measurement of the PSF is available. Given a set of PSFs observed at random locations, we want to estimate the PSFs at galaxies locations for shape measurement correction. We propose an interpolation framework based on sliced optimal transport. A nonlinear dimension reduction is first performed based on local pairwise approximated Wasserstein distances. A low dimensional representation of the unknown PSFs is then estimated, which in turn is used to derive representations of those PSFs in the Wasserstein metric. Finally, the interpolated PSFs are calculated as approximated Wasserstein barycenters. The proposed method was tested on simulated monochromatic PSFs of the Euclid space mission telescope (to be launched in 2020). It achieves remarkable accuracy in terms of pixel values and shape compared to standard methods such as inverse distance weighting or radial basis function based interpolation methods.<\/jats:p>","DOI":"10.1137\/16m1093677","type":"journal-article","created":{"date-parts":[[2017,9,14]],"date-time":"2017-09-14T13:22:00Z","timestamp":1505395320000},"page":"1549-1578","source":"Crossref","is-referenced-by-count":10,"title":["Point Spread Function Field Learning Based on Optimal Transport Distances"],"prefix":"10.1137","volume":"10","author":[{"given":"F.","family":"Ngol\u00e9","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.-L.","family":"Starck","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,9,14]]},"reference":[{"key":"atypb1","unstructured":"H. Abdi,\n                      Metric Multidimensional Scaling\n                      , in Encyclopedia of Measurement and Statistics, N. J. Salkind, ed., SAGE, Thousand Oaks, CA, 2007, pp. 598-605."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-014-0506-3"},{"key":"atypb3","first-page":"142","volume":"17","author":"Bottou L.","year":"1998","journal-title":"On-line Learning Neural Networks"},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"R. Burkard, M. Dell'Amico, and S. Martello,\n                      Assignment Problems\n                      , SIAM, Philadelphia, 2009.","DOI":"10.1137\/1.9780898717754"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2009.10.014"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1109\/34.990137"},{"key":"atypb7","first-page":"431","author":"M. Cropper","year":"2013","journal-title":"Monthly Not. Roy. Astronomical Soc."},{"key":"atypb8","unstructured":"M. Cuturi and A. Doucet,\n                      Fast computation of Wasserstein barycenters\n                      , in Proceedings of the 31st International Conference on Machine Learning, 2014, pp. 685-693."},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2015.2398954"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1031596100"},{"key":"atypb11","unstructured":"D. Eberly,\n                      Thin Plate Splines\n                      , Geometric Tools, Chapel Hill, NC, 2002."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.2307\/2323093"},{"key":"atypb13","unstructured":"Euclid: Mapping the Geometry of the Dark Universe\n                      , Tech. report, ESA, Paris, 2011."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.cviu.2015.02.008"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0312(199801)51:1<23::AID-CPA2>3.0.CO;2-H"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1051\/0004-6361\/201219739"},{"key":"atypb17","unstructured":"J. W. Goodman,\n                      Introduction to Fourier Optics\n                      , Roberts and Company Publishers, Englewood, CO, 2005."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/55.3.582"},{"key":"atypb19","first-page":"261","author":"Gramfort A.","year":"2015","journal-title":"New York"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1023\/B:VISI.0000036836.66311.97"},{"key":"atypb21","unstructured":"M. Jarvis and B. Jain,\n                      Principal Component Analysis of PSF Variation in Weak Lensing Surveys\n                      ,arXiv:astro-ph\/0412234, 2004."},{"key":"atypb22","unstructured":"M. Jarvis, P. Schechter, and B. Jain,\n                      Telescope Optics and Weak Lensing: PSF Patterns due to Low Order Aberrations\n                      ,arXiv:0810.0027v1, 2008."},{"key":"atypb23","first-page":"1403","volume":"119","author":"Jee M. J.","year":"2007","journal-title":"Pacific"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1086\/176071"},{"key":"atypb25","first-page":"199","volume":"321","author":"Kantorovich L. V.","year":"1942","journal-title":"C.R. Acad. Sci. USSR"},{"key":"atypb26","first-page":"761","author":"Kolesov I.","year":"2010","journal-title":"Proceedings of the IEEE International Conference on Image Processing"},{"key":"atypb27","first-page":"29","author":"Kuhn H. W.","year":"2009","journal-title":"New York"},{"key":"atypb28","first-page":"85","author":"Little A. V.","year":"2009","journal-title":"Proceedings of the IEEE\/SP 15th Workshop on Statistical Signal Processing"},{"key":"atypb29","unstructured":"J. I. 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Bronstein, eds., Lecture Notes in Comput. Sci., 6667, Springer, New York, 2011, pp. 435-446.","DOI":"10.1007\/978-3-642-24785-9_37"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-8711.2003.05901.x"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1051\/0004-6361\/200912654"},{"key":"atypb39","unstructured":"H. F. Stabenau, B. Jain, G. Bernstein, and M. Lampton,\n                      Lensing Systematics from Space: Modeling PSF Effects in the SNAP Survey\n                      ,arXiv:0710.3355 [astro-ph], 2007."},{"key":"atypb40","doi-asserted-by":"crossref","unstructured":"A. B. Suksmono,\n                      Reconstruction of Complex-Valued Fractional Brownian Motion Fields Based on Compressive Sampling and Its Application to PSF Interpolation in Weak Lensing Survey\n                      ,arXiv:1311.0124 [cs. 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