Optical Engineering, vol. 31, issue 12 (1992) pp. 2572-2579
The multidimensional inverse scattering of objects buried in an inhomogeneous elastic background structure is studied. The entire medium, comprising inclusion and background, is probed by an ultrasonic force, and the field scattered by the object 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. Because the multidimensional inverse scattering problem is nonlinear and ill-posed, it is linearized within the Born approximation for inhomogeneous background, and a minimum-norm least-squares 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-squares inversion of the object is performed from synthetic data. A Tikhonov regularization scheme is also examined and compared to the minimum-norm least-squares estimate.
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