{"id":170,"date":"2016-10-01T21:43:05","date_gmt":"2016-10-01T19:43:05","guid":{"rendered":"https:\/\/project.inria.fr\/rarl2\/?page_id=170"},"modified":"2016-10-03T21:30:18","modified_gmt":"2016-10-03T19:30:18","slug":"source-recovery","status":"publish","type":"page","link":"https:\/\/project.inria.fr\/rarl2\/use\/source-recovery\/","title":{"rendered":"Source recovery"},"content":{"rendered":"<p>From measurements by electrodes of the electric potential on the scalp, the problem is to recover a distribution of pointwise dipolar current<br \/>\nsources with moments located in the brain (modeling the presence of epileptic foci). The head is modeled as a set of three spherical nested regions (brain, skull, scalp) and in each region constant conductivities are assumed. A macroscopic model and quasi-static approximation of Maxwell-equations are used to describe the spacial behavior of the potential.<br \/>\nThe inverse problem can be approached in two steps:<\/p>\n<ul>\n<li>get the anti-harmonic part of the potential from the data using propagation techniques<\/li>\n<li>recover the localizations and the moments of the sources by rational approximation on planar sections (RARL2)<\/li>\n<\/ul>\n<p><a href=\"https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/approx_ration2.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/approx_ration2.png\" alt=\"approx_ration2\" width=\"746\" height=\"517\" class=\"aligncenter size-full wp-image-221\" srcset=\"https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/approx_ration2.png 746w, https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/approx_ration2-300x208.png 300w, https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/approx_ration2-216x150.png 216w, https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/approx_ration2-150x104.png 150w\" sizes=\"auto, (max-width: 746px) 100vw, 746px\" \/><\/a><br \/>\nThe singularities (green) of the potential are aligned and the sources (black) correspond to the maximum modulus. The rational approximations (pink) accumulate to these singularities:<\/p>\n<table>\n<tbody>\n<tr>\n<td>\n<a href=\"https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/poster2S1z.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-224\" src=\"https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/poster2S1z.png\" alt=\"poster2s1z\" width=\"500\" height=\"400\" srcset=\"https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/poster2S1z.png 500w, https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/poster2S1z-300x240.png 300w, https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/poster2S1z-188x150.png 188w, https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/poster2S1z-150x120.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a>\n<\/td>\n<td>\n<a href=\"https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/poster2S1d.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-223\" src=\"https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/poster2S1d.png\" alt=\"poster2s1d\" width=\"500\" height=\"400\" srcset=\"https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/poster2S1d.png 500w, https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/poster2S1d-300x240.png 300w, https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/poster2S1d-188x150.png 188w, https:\/\/project.inria.fr\/rarl2\/files\/2016\/10\/poster2S1d-150x120.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a>\n<\/td>\n<\/tr>\n<\/table>\n<\/tbody>\n<p>One of the advantages of this method is that <em>it does not require the a priori knowledge of the exact number of sources<\/em>. If the order of the approximation is larger than the number of sources, the extra poles accumulate to the boundary of he disks. For this application, the software RARL2 has been modified to impose triple poles for the approximant. The whole process is handled by the software <a href=\"http:\/\/www-sop.inria.fr\/apics\/FindSources3D\/en\/index.html\"> FindSources3d <\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>From measurements by electrodes of the electric potential on the scalp, the problem is to recover a distribution of pointwise dipolar current sources with moments located in the brain (modeling the presence of epileptic foci). The head is modeled as a set of three spherical nested regions (brain, skull, scalp)\u2026<\/p>\n<p> <a class=\"continue-reading-link\" href=\"https:\/\/project.inria.fr\/rarl2\/use\/source-recovery\/\"><span>Continue reading<\/span><i class=\"crycon-right-dir\"><\/i><\/a> <\/p>\n","protected":false},"author":40,"featured_media":0,"parent":117,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-170","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/pages\/170","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/users\/40"}],"replies":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/comments?post=170"}],"version-history":[{"count":8,"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/pages\/170\/revisions"}],"predecessor-version":[{"id":248,"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/pages\/170\/revisions\/248"}],"up":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/pages\/117"}],"wp:attachment":[{"href":"https:\/\/project.inria.fr\/rarl2\/wp-json\/wp\/v2\/media?parent=170"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}