{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/imaging-of-isotropic-and-anisotropic","title":"Imaging of isotropic and anisotropic conductivities from power densities in three dimensions","arxiv_id":"1711.03137","date":"2017-11-08","proceeding":null,"authors":["François Monard","Donsub Rim"],"abstract":"We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality Ultrasound Modulated Electrical Impedance Tomography for instance. We improve on the algorithms previously derived in [Bal et al, Inverse Probl Imaging (2013), pp.353-375, Monard and Bal, Comm. PDE (2013), pp.1183-1207] for both isotropic and anisotropic cases, and we address the well-known issue of vanishing determinants in particular. The algorithm is implemented and we provide numerical results that illustrate the improvements.","url_abs":"http://arxiv.org/abs/1711.03137v3","url_pdf":"http://arxiv.org/pdf/1711.03137v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"imaging-of-isotropic-and-anisotropic","repo_url":"https://github.com/dsrim/powerdensity3d","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}