Acoustic inverse scattering using topological derivative of far-field measurements-based \(L^2\) cost functionals (Q2861883)

The paper is concerned with the theoretical aspects of the use of the topological derivative as a qualitative inversion tool for wave-based identification of finite-size objects. The available data is assumed to consist of measurements of scattered far-field patterns, gathered into the far-field operator. An inhomogeneous medium and a finite number of point-like scatters are considered, using either the Born approximation or a full scattering model. The behavior of the indicator function provided by the topological derivative of the least-squares cost functional is studied depending on the location of the sampling point, the choice of the trial refraction index featured in the asymptotic analysis of the cost functional and the values of characteristic frequency, contrast and obstacle size. Semi-analytical and numerical examples are presented. The topological derivative approach is discussed and compared to other sampling methods.