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An inverse medium problem for scanning acoustic microscopy
Author(s) -
Clason Christian,
Beilina Larisa
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510300
Subject(s) - inverse problem , visualization , uniqueness , computer science , process (computing) , microscopy , acoustic microscopy , set (abstract data type) , inverse , acoustics , materials science , mathematics , optics , artificial intelligence , physics , mathematical analysis , geometry , programming language , operating system
For nondestructive testing of materials, the scanning acoustic microscope is commonly used for the qualitative visualization of elastic properties. However, especially for medical applications, quantitative evaluation of the measured data is of considerable interest. Based on a mathematical model of the process of scanning acoustic microscopy, the problem of recovering elastomechanical parameters of human bone can be cast into the form of identifying the unknown space‐dependent speed of sound in the three‐dimensional acoustic wave equation. Specific methods have to be devised for this kind of inverse medium problem due to the reduced set of measured data available. Here, an optimal control approach is used. We discuss uniqueness and stability of the reconstruction and present a numerical example. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)