Gryazin, Yuriy A.; Klibanov, Michael V.; Lucas, Thomas R. Imaging the diffusion coefficient in a parabolic inverse problem in optical tomography. (English) Zbl 0926.35160 Inverse Probl. 15, No. 2, 373-397 (1999). 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. Cited in 10 Documents MSC: 35R30 Inverse problems for PDEs 35K15 Initial value problems for second-order parabolic equations 92C55 Biomedical imaging and signal processing Keywords:reconstruction of the diffusion coefficient; optical imaging of small abnormalities hidden in a random media, such as biological tissues, foggy atmospheres, murky water PDFBibTeX XMLCite \textit{Y. A. Gryazin} et al., Inverse Probl. 15, No. 2, 373--397 (1999; Zbl 0926.35160) Full Text: DOI