Imaging by modification: numerical reconstruction of local conductivities from corresponding power density measurements

Yves Capdeboscq (1) , Jérôme Fehrenbach (2) , Frédéric de Gournay (3) , Otared Kavian (3)

1 MI - Mathematical Institute [Oxford]
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 LMV - Laboratoire de Mathématiques de Versailles

We discuss the reconstruction of the impedance from the local power density. This study is motivated by a new imaging principle which allows to recover interior measurements of the energy density by a non invasive method. We discuss the theoretical feasibility in two dimensions, and propose numerical algorithms to recover the conductivity in two and three dimension. The efficiency of this approach is documented by several numerical simulations

Mots clés: Inverse problem; conductivity; imaging

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Yves Capdeboscq, Jérôme Fehrenbach, Frédéric de Gournay, Otared Kavian. Imaging by modification: numerical reconstruction of local conductivities from corresponding power density measurements. SIAM Journal on Imaging Sciences, 2009, 2 (4), pp.1003--1030. ⟨10.1137/080723521⟩. ⟨hal-00280599v2⟩