{"paper":{"title":"A convergent algorithm for the hybrid problem of reconstructing conductivity from minimal interior data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Adrian Nachman, Alexandre Timonov, Amir Moradifam","submitted_at":"2011-12-09T01:58:38Z","abstract_excerpt":"We consider the hybrid problem of reconstructing the isotropic electric conductivity of a body $\\Omega$ from interior Current Density Imaging data obtainable using MRI measurements. We only require knowledge of the magnitude $|J|$ of one current generated by a given voltage $f$ on the boundary $\\partial\\Omega$. As previously shown, the corresponding voltage potential u in $\\Omega$ is a minimizer of the weighted least gradient problem\n  \\[u=\\hbox{argmin} \\{\\int_{\\Omega}a(x)|\\nabla u|: u \\in H^{1}(\\Omega), \\ \\ u|_{\\partial \\Omega}=f\\},\\] with $a(x)= |J(x)|$. In this paper we present an alternati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1998","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}