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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 =div(D(x)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:
35R30Inverse problems for PDE
35K15Second order parabolic equations, initial value problems
92C55Biomedical imaging and signal processing, tomography