Imaging sound-soft targets in waveguides using the topological derivative

Abstract We investigate the use of shape sensitivity analysis based on topological derivatives to image a non-penetrable obstacle located inside a tubular acoustic waveguide. Assuming time-harmonic wave propagation, we reduce the problem to a finite section of pipe using the Dirichlet-to-Neumann map, and derive a closed form expression of the topological derivative for this situation. We investigate the method numerically on synthetic data. A particular feature of our study is the use of multi-frequency data.

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