Automatic recognition of multidimensional objects buried in layered elastic background media

Abstract

This study focuses on the multidimensional inverse scattering of objects buried in an inhomogeneous elastic bac kground structure. Die medium is probed by an ultrasonic force and (lie scattered field is observed along a receiver array. Tlie 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 multidimensional inverse scattering problem being nonlinear and ill-posed, it 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. A priori information can be incorporated into the algorithm to enhance the accuracy and improve the resolution of the recovered object characteristics. 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 also examined and compared to the minimum-norm least-square estimate.