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Time domain topological gradient and time reversal analogy: an inverse method for ultrasonic target detection. (English) Zbl 1189.74070
Summary: To find the shape and position of one or several obstacles embedded in a 2D or 3D elastic medium given ultrasonic measurements performed with a linear array of sensors, we use a topological gradient method. It consists in minimizing a cost function which evaluates the adequation between the measurements obtained for the inspected medium and measurements performed on a reference medium known as safe. The topological gradient is a function of both the solutions of the forward and adjoint problems. The mathematical solution of such an adjoint problem corresponds to a physical time reversal operation. This inverse method is therefore physically justified and inheritance of the refocusing properties of the time reversal phenomenon is expected.

74J25 Inverse problems for waves in solid mechanics
74J20 Wave scattering in solid mechanics
Full Text: DOI
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