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Imaging by modification: numerical reconstruction of local conductivities from corresponding power density measurements. (English) Zbl 1180.35549

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

MSC:

35R30 Inverse problems for PDEs
74B05 Classical linear elasticity
92C55 Biomedical imaging and signal processing
68U10 Computing methodologies for image processing
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
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