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- W2078392761 abstract "We investigate the problem of reconstructing a fully anisotropic conductivity tensor $gamma$ from internal functionals of the form $nabla ucdotgammanabla u$ where $u$ solves $nablacdot(gammanabla u) = 0$ over a given bounded domain $X$ with prescribed Dirichlet boundary condition. This work motivated by hybrid medical imaging methods covers the case $nge 3$, following the previously published case $n=2$ cite{Monard2011}. Under knowledge of enough such functionals, and writing $gamma = tau tilde gamma$ ($det tildegamma = 1$) with $tau$ a positive scalar function, we show that all of $gamma$ can be explicitely and locally reconstructed, with no loss of scales for $tau$ and loss of one derivative for the anisotropic structure $tildegamma$. The reconstruction algorithms presented require rank maximality conditions that must be satisfied by the functionals or their corresponding solutions, and we discuss different possible ways of ensuring these conditions for $C^{1,alpha}$-smooth tensors ($0<alpha<1$)." @default.
- W2078392761 created "2016-06-24" @default.
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- W2078392761 date "2012-08-29" @default.
- W2078392761 modified "2023-10-18" @default.
- W2078392761 title "Inverse anisotropic conductivity from power densities in dimension $nge 3$" @default.
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