{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T12:24:14Z","timestamp":1783686254163,"version":"3.55.0"},"reference-count":25,"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>The inverse conductivity problem is the mathematical problem that must be solved in order for electrical impedance tomography systems to be able to make images. Here we show how this inverse conductivity problem is related to a number of other inverse problem. We then explain the workings of an algorithm that we have used to make images from electrical impedance data measured on the boundary of a circle in two dimensions. This algorithm is based on the method of least squares. It takes one step of a Newton's method, using a constant conductivity as an initial guess. Most of the calculations can therefore be done analytically. The resulting code is named NOSER, for Newton's One\u2010Step Error Reconstructor. It provides a reconstruction with 496 degrees of freedom. The code does not reproduce the conductivity accurately (unless it differs very little from a constant), but it yields useful images. This is illustrated by images reconstructed from numerical and experimental data, including data from a human chest.<\/jats:p>","DOI":"10.1002\/ima.1850020203","type":"journal-article","created":{"date-parts":[[2007,3,5]],"date-time":"2007-03-05T22:30:08Z","timestamp":1173133808000},"page":"66-75","source":"Crossref","is-referenced-by-count":523,"title":["NOSER: An algorithm for solving the inverse conductivity problem"],"prefix":"10.1002","volume":"2","author":[{"given":"M.","family":"Cheney","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D.","family":"Isaacson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. C.","family":"Newell","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Simske","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"Goble","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2005,10,20]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Inverse Problems in Partial Differential Equations","author":"Barber D. C.","year":"1990"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/10.7289"},{"key":"e_1_2_1_4_2","volume-title":"Review of Progress in Quantitative NDE","author":"Eggleston M. R.","year":"1989"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"Clin. Phys. Phys. Meas. 1987 8 Suppl. A Electrical Impedance Tomography\u2014Applied Potential Tomography","DOI":"10.1088\/0143-0815\/8\/4A\/301"},{"key":"e_1_2_1_6_2","volume-title":"Inverse Problems in Partial Differential Equations","author":"Isaacson D.","year":"1990"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/1971435"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160390106"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160380513"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/3\/4\/003"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01224129"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0161-7346(84)90025-7"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1109\/10.35300"},{"key":"e_1_2_1_14_2","unstructured":"S. J.Simske \u201cAn adaptive current determination and a one\u2010step reconstruction technique for a current tomography system \u201d M. S. thesis R. P. I. Troy NY 1987."},{"key":"e_1_2_1_15_2","article-title":"Electric current computed tomography and eigenvalues","author":"Gisser D. G.","journal-title":"SIAM J. Appl. Math."},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1109\/TMI.1986.4307752"},{"key":"e_1_2_1_17_2","volume-title":"Numerical Recipes","author":"Press W. H.","year":"1986"},{"key":"e_1_2_1_18_2","unstructured":"T. J.Yorkey \u201cComparing reconstruction methods for electrical impedance tomography \u201d Ph. D. thesis University of Winconsin Madison WI 1986."},{"key":"e_1_2_1_19_2","unstructured":"R.KohnandA.McKenney \u201cNumerical implementation of a variational method for electrical impedance tomography \u201d preprint."},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.1364\/AO.24.003985"},{"key":"e_1_2_1_21_2","doi-asserted-by":"crossref","unstructured":"F.SantosaandM.Vogelius \u201cA backprojection algorithm for electrical impedance imaging \u201d Technical Note BN 1081 Dept. of Mathematics University of Maryland College Park MD 1988.","DOI":"10.21236\/ADA198680"},{"key":"e_1_2_1_22_2","unstructured":"P.Hua \u201cReconstruction methods for electrical impedance tomography \u201d Ph. D. thesis University of Wisconsin Madison WI 1989."},{"key":"e_1_2_1_23_2","volume-title":"Analysis of Numerical Methods","author":"Isaacson E.","year":"1966"},{"key":"e_1_2_1_24_2","unstructured":"E. W.CheneyandD.Kincaid Numerical Mathematics and Computing Brooks\/Cole Monterey CA 1980."},{"key":"e_1_2_1_25_2","volume-title":"Numerical Methods for Unconstrained Optimization and Nonlinear Equations","author":"Dennis J.","year":"1983"},{"key":"e_1_2_1_26_2","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160370302"}],"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.1850020203","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/ima.1850020203","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T18:29:49Z","timestamp":1697999389000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/ima.1850020203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,6]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,6]]}},"alternative-id":["10.1002\/ima.1850020203"],"URL":"https:\/\/doi.org\/10.1002\/ima.1850020203","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]]}}}