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Numerische und
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In current public discussions, much attention is paid to the danger of breast cancer. X-Ray methods for cancer detection like mammography are considered inappropriate. Recently, novel optical and acoustical methods are being examined. One of these is image reconstruction from time-harmonic ultrasound data, which requires determination of the coefficient f in the Helmholtz equation Delta u+k^2 (1+f) u=0 from boundary measurement of various solutions u of the equation for different boundary conditions. In this equation, f determines the physical properties of the scatterer, while k is the wave number and u is the time-harmonic sound wave. Born- and Rytov-aproximations have been used for some time to accomplish this task, but are not precise enough. All functions may be either 2D or 3D, depending on the application. To overcome the complexity problems, an iterative algorithm that works on finite data and incorporates finite boundary conditions instead of radiation condition is presented.
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