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Imaging the diffusion coefficient in a parabolic inverse problem in optical tomography. (English) Zbl 0926.35160

Summary: The elliptic systems method, previously developed by the second and third authors, is extended to the reconstruction of the diffusion coefficient of an inverse problem for the parabolic equation \(u_t= \text{div}(D(x)\nabla u)\) in the \(n\)-dimensional case \((n= 2,3)\). This inverse problem has applications to optical imaging of small abnormalities hidden in a random media, such as biological tissues, foggy atmospheres, murky water, etc. Results of numerical experiments are presented in the two-dimensional case, for realistic ranges of the parameters.

MSC:

35R30 Inverse problems for PDEs
35K15 Initial value problems for second-order parabolic equations
92C55 Biomedical imaging and signal processing
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