Global convexity in a single-source 3-D inverse scattering problem |
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Authors: | GUTMAN SEMION; KLIBANOV MICHAEL V; TIKHONRAVOV ALEXANDER V |
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Institution: |
Department of Mathematics, University of Oklahoma Norman, Oklahoma 73019, USA
Department of Mathematics, University of North Carolina at Charlotte Charlotte, North Carolina 28223, USA
Scientific Research Computing Center at Moscow State University Moscow 119 899, Russia
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Abstract: | The authors consider nonoverdetermined 3-D inverse scatteringproblems based on the telegraph equation
The goal is to recover the media properties represented by thecoefficients a(x) or b(x) from, for example, backscatteringdata. Such a problem models imaging in certain biological tissues,in murky water, and in some geophysical and atmospheric phenomena.The main restriction is in the consideration of only finitelymany Fourier harmonics of the solution u(x, t) (in the timevariable t only). This seems to be acceptable for practicalcomputations. The main mathematical tool is the constructionof uniformly convex cost functionals on compact convex subsetsof the solutions. This assures a global convergence of the minimizationalgorithm, which can be applied in the case of large media inhomogeneities.Since the technique is based on the so-called Carleman's weightfunctions, the approach is called Carleman's weight method. |
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Keywords: | |
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