Inverse scattering using a spectral domain moment method and non-linear optimization

Summary form only given. The problem of inverse scattering is a fundamental one in the field of mathematical physics and consists of finding the refractive index distribution of an inhomogeneous medium from the knowledge of the scattered field away from the medium, assuming that the incident wave is known. In this work, a novel inverse scattering method based on a spectral domain method of moments technique is presented, suitable for biological objects imaging. The interaction of the incident field with the scattering object is described in terms of the Lippmann-Schwinger scattering integral equation. The unknown total wavefield inside the scattering object is expressed as a superposition of a relatively small number of global domain basis functions (i.e. plane waves), while the unknown object function is expanded in a set of spatially shifted Gaussian basis functions. The inverse scattering problem is formulated as a non-linear optimization problem where the cost function to be minimized consists of two terms. The first term represents the error in satisfying the equation for the field inside the scattering object, while the second term represents the difference between the measured value of the scattered field and the theoretic prediction. Two different optimization techniques are employed, namely the modified gradient and the quasi-Newton method and their performance is compared in terms of convergence speed and accuracy of the reconstruction. A number of numerical simulations are performed in order to assess the performance of the optimization methods employed, using models of lossy and non-lossy, two-dimensional scattering objects.