Ultrasonic inverse scattering of multidimensional objects buried in multilayered elastic background structures

The authors focus on the multidimensional inverse scattering of objects buried in an inhomogeneous elastic background structure. The medium is probed by an ultrasonic force and the scattered field is observed along a receiver array. The goal is to retrieve both the geometry (imaging problem) and the constitutive parameters (inverse problem) of the object through an appropriate multiparameter direct linear inversion. The problem is cast in terms of a vector integral equation elastic scattering framework. The multidimensional inverse scattering problem, being nonlinear and ill-posed, is linearized within the Born approximation for inhomogeneous background, and a minimum-norm least-square solution to the discretized version of the vector integral formulation is sought. The solution is based on a singular value decomposition of the forward operator matrix. The method is illustrated on a 2-D problem where constrained least-square inversion of the object is performed from synthetic data. A Tikhonov regularization scheme is examined and compared to the minimum-norm least-square estimate.