Direct and Inverse Scattering In 3-D Fluid Media

Abstract

Since a few years now, we have been involved in ultrasonic imaging of inhomogeneous 2-D fluid media from experimental and synthetically generated data by means of diffraction tomography [1, 2]. We investigate herein transmission mode diffraction tomography of 3-D media from single-frequency multiview synthetic data. Two different techniques are considered. First, we apply a Fourier domain interpolation technique [3] derived from the “generalized projection slice theorem” which provides images of the object under investigation in a very efficient way, as it is based upon FFT algorithms. However, when the weak scattering approximations (Born’s and Rytov’s ones) fail, no quantitative information on the object parameters can be inferred from these images, as the reconstructed quantity depends both on the field and on the parameters. Such a quantitative information can be obtained with the second technique presented here. It is based upon an iterative solution of the non-linear ill-posed inverse scattering problem [4,5], through a linearization and a Tikhonov regularization procedure [6,7]. This technique is much more time consuming than the first one. However, the convergence of the iterative process can be speeded-up by introducing “a priori” information (which can be obtained from the first technique) in the initial guess of the solution required by the process.