{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T20:08:08Z","timestamp":1790712488266,"version":"4.1.0"},"reference-count":65,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100004097","name":"Fondation ARC pour la Recherche sur le Cancer","doi-asserted-by":"publisher","award":["MIMMOSA"],"award-info":[{"award-number":["MIMMOSA"]}],"id":[{"id":"10.13039\/501100004097","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007267","name":"Centre International de Math\u00c3\u00a9matiques et Informatique de Toulouse","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007267","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2016,1]]},"abstract":"<jats:p>Magnetic resonance imaging (MRI) is probably one of the most successful application fields of compressed sensing. Despite recent advances, there is still a large discrepancy between theories and most actual implementations. Overall, many important questions related to sampling theory remain open. In this paper, we attack one of them: given a set of sampling constraints (e.g., measuring Fourier coefficients along physically plausible trajectories), how to optimally design a sampling pattern? We first outline three aspects that should be carefully designed by inspecting the literature, namely admissibility, limit of the empirical measure, and coverage speed. To address them jointly, we then propose an original approach which consists of projecting a probability distribution onto a set of admissible measures. The proposed algorithm permits handling arbitrary constraints and automatically generates efficient sampling patterns for MRI as shown on realistic simulations. We achieve a 20-fold undersampling factor at very high 2D resolution (100 $\\mu$m isotropic) on physically plausible sampling trajectories with a gain in SNR of 2--3 dB on reconstructed MR images as compared to more standard sampling patterns (e.g., radial, spiral).<\/jats:p>","DOI":"10.1137\/16m1059205","type":"journal-article","created":{"date-parts":[[2016,12,6]],"date-time":"2016-12-06T12:12:44Z","timestamp":1481026364000},"page":"2039-2072","source":"Crossref","is-referenced-by-count":48,"title":["On the Generation of Sampling Schemes for Magnetic Resonance Imaging"],"prefix":"10.1137","volume":"9","author":[{"given":"Claire","family":"Boyer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicolas","family":"Chauffert","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Philippe","family":"Ciuciu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jonas","family":"Kahn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pierre","family":"Weiss","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2016,12,6]]},"reference":[{"key":"atypb1","unstructured":"B. Adcock, A. Hansen, C. Poon, and B. Roman,\n                      Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing\n                      , 2013."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2012.2215837"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/080716542"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2016.2524628"},{"key":"atypb5","unstructured":"C. Boyer, J. Bigot, and P. Weiss,\n                      Compressed sensing with structured sparsity and structured acquisition\n                      , preprint,https:\/\/arxiv.org\/abs\/1505.01619, 2015."},{"key":"atypb6","first-page":"66","author":"Boyer C.","year":"2012","journal-title":"Spain"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/130941560"},{"key":"atypb8","first-page":"22","author":"Bridson R.","year":"2007","journal-title":"ACM New York"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.22100"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20124"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.885507"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2161794"},{"key":"atypb13","unstructured":"N. Chauffert,\n                      Compressed sensing along physicaly plausible sampling trajectories\n                      , Ph.D. thesis, Universite\u0301 Paris-Sud, Orsay, France, 2015."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/130946642"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"N. Chauffert, P. Ciuciu, J. Kahn, and P. Weiss,\n                      A projection method on measure sets\n                      , Constructive Approximation, in press,https:\/\/doi.org\/10.1007\/s00365-016-9346-2.","DOI":"10.1007\/s00365-016-9346-2"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"N. Chauffert, P. Ciuciu, and P. Weiss,\n                      Variable density compressed sensing in MRI. Theoretical vs. heuristic sampling strategies\n                      , in Proceedings of the 10th IEEE ISBI Conference on Biomedical Imaging, San Francisco, CA, 2013, pp. 298-301.","DOI":"10.1109\/ISBI.2013.6556471"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2016.2544251"},{"key":"atypb18","first-page":"10","volume":"6","author":"Curtis A. T.","year":"2008","journal-title":"Int. J. Biomed. Imaging"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2006.871582"},{"key":"atypb20","doi-asserted-by":"crossref","unstructured":"D. D. Liu, D. Liang, X. Liu, and Y.T. Zhang,\n                      Under-sampling trajectory design for compressed sensing MRI\n                      , in 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2012, pp. 73-76,https:\/\/doi.org\/10.1109\/EMBC.2012.6345874.","DOI":"10.1109\/EMBC.2012.6345874"},{"key":"atypb21","first-page":"1313","volume":"23","author":"Fatterpekar G. M.","year":"2002","journal-title":"Am. J. Neuroradiol."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1109\/MCSE.2012.40"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2014.11.002"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2011.2140121"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2011.2174158"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2010.2085084"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.10666"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1109\/42.97598"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1145\/1555386.1555388"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1155\/2007\/24727"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2013.2288004"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1080\/03052150701641783"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1038\/242190a0"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.21391"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2008.922699"},{"key":"atypb36","first-page":"685","author":"Lustig M.","year":"2005","journal-title":"Miami, FL"},{"key":"atypb37","first-page":"1","author":"Ma S.","year":"2008","journal-title":"Washington, DC"},{"key":"atypb38","first-page":"287","volume":"76","author":"Maudsley A. A.","year":"1988","journal-title":"J. Magn. Reson."},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.20163"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2012.2188039"},{"key":"atypb41","first-page":"372","volume":"27","author":"Nesterov Y.","year":"1983","journal-title":"Soviet Math. Dokl."},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-012-0629-5"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.1910330414"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.1985.4307723"},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1522-2594(199911)42:5<952::AID-MRM16>3.0.CO;2-S"},{"key":"atypb46","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2011.2173698"},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1186\/1687-6180-2012-6"},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2011.2163712"},{"key":"atypb49","doi-asserted-by":"publisher","DOI":"10.1109\/IEMBS.2011.6090639"},{"key":"atypb50","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2010.2090538"},{"key":"atypb51","unstructured":"B. Roman, A. Hansen, and B. Adcock,\n                      On asymptotic structure in compressed sensing\n                      , preprinthttps:\/\/arxiv.org\/abs\/1406.4178, 2014."},{"key":"atypb52","doi-asserted-by":"publisher","DOI":"10.1137\/08072975X"},{"key":"atypb53","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2010.01716.x"},{"key":"atypb54","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1002\/mrm.22180","volume":"63","author":"Seeger M.","year":"2010","journal-title":"Magn. Reson. Med."},{"key":"atypb55","doi-asserted-by":"publisher","DOI":"10.1007\/BF03025291"},{"key":"atypb56","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.1910380414"},{"key":"atypb57","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.1910340316"},{"key":"atypb58","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.20626"},{"key":"atypb59","doi-asserted-by":"publisher","DOI":"10.1137\/100790197"},{"key":"atypb60","doi-asserted-by":"publisher","DOI":"10.1118\/1.595331"},{"key":"atypb61","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2012.2232346"},{"key":"atypb62","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.25841"},{"key":"atypb63","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.25303"},{"key":"atypb64","doi-asserted-by":"crossref","unstructured":"S. S. Vasanawala, M. J. Murphy, M. T. Alley, P. Lai, K. Keutzer, J. M. Pauly, and M. Lustig,\n                      Practical parallel imaging compressed sensing MRI: Summary of two years of experience in accelerating body MRI of pediatric patients\n                      , in 2011 IEEE International Symposium on Biomedical Imaging, 2011, pp. 1039-1043,https:\/\/doi.org\/10.1109\/ISBI.2011.5872579.","DOI":"10.1109\/ISBI.2011.5872579"},{"key":"atypb65","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.2006.885337"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1059205","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:27:36Z","timestamp":1787322456000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1059205"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1]]},"references-count":65,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,1]]}},"alternative-id":["10.1137\/16M1059205"],"URL":"https:\/\/doi.org\/10.1137\/16m1059205","relation":{},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1]]}}}