{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T01:01:56Z","timestamp":1773622916556,"version":"3.50.1"},"reference-count":11,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2005,10,20]],"date-time":"2005-10-20T00:00:00Z","timestamp":1129766400000},"content-version":"vor","delay-in-days":5620,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int J Imaging Syst Tech"],"published-print":{"date-parts":[[1990,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Inverse scattering methods for reconstructing sound\u2010wave\u2010speed structure in the dimensions have been shown to be equivalent to inverting line integrals when the scattered field is of sufficiently high frequency and the scattering is sufficiently weak. Seismic traveltime tomography uses first arrival traveltime data to invert for wave\u2010speed structure. Of course, the traveltime is itself a line integral along a refracting ray path through the medium being probed. The similarity between these two inversion problems is discussed. One type of neural network\u2010the Hopfield net\u2010may be used to improve the traveltime inversion. We find that, by taking advantage of the general relationship between least\u2010squares solution and generalized inverses, the neural networks approach eliminates the need for inverting singular or poorly conditioned matrices and therefore also eliminates the need for the damping term often used to regularize such inversions. This procedure produces reconstructions with fewer artifacts and faster convergence than those attained previously using damped least\u2010squares methods.<\/jats:p>","DOI":"10.1002\/ima.1850020206","type":"journal-article","created":{"date-parts":[[2007,3,5]],"date-time":"2007-03-05T22:30:08Z","timestamp":1173133808000},"page":"112-118","source":"Crossref","is-referenced-by-count":9,"title":["Inverse scattering, seismic traveltime tomography, and neural networks"],"prefix":"10.1002","volume":"2","author":[{"given":"Shin\u2010Yee","family":"Lu","sequence":"first","affiliation":[]},{"given":"James G.","family":"Berryman","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2005,10,20]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/4\/2\/008"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.81.10.3088"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/BF00339943","article-title":"Neural computation of decisions in optimization problems","volume":"52","author":"Hopfield J. J.","year":"1985","journal-title":"Biol. Cybernet."},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"W.LiandN. M.Nasrabadi \u201cObject recognition based on graph mathing implemented by a Hopfield\u2010style neural network \u201d in:Proceedings of the International Joint Conference on Neural Networks Washington DC June1989 pp.II\u2010287\u2013290.","DOI":"10.1109\/IJCNN.1989.118712"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1086\/164700"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1979.11390"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/36.17671"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100030929"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.62.2953"},{"key":"e_1_2_1_11_2","volume-title":"Image Reconstruction from Projections","author":"Herman G. T.","year":"1980"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.6028\/jres.049.044"}],"container-title":["International Journal of Imaging Systems and Technology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fima.1850020206","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/ima.1850020206","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T18:30:07Z","timestamp":1697999407000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/ima.1850020206"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,6]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,6]]}},"alternative-id":["10.1002\/ima.1850020206"],"URL":"https:\/\/doi.org\/10.1002\/ima.1850020206","archive":["Portico"],"relation":{},"ISSN":["0899-9457","1098-1098"],"issn-type":[{"value":"0899-9457","type":"print"},{"value":"1098-1098","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,6]]}}}