A fast method for acoustic imaging of multiple three-dimensional objects

Abstract

This paper is concerned with the inverse problem for imaging multiple three-dimensional objects using the information of the far-field pattern of the scattered wave. A spatially dependent function, which has noticeably different values inside and outside the obstacle, is derived. A numerical method based on the characterization is developed to obtain a visualization of the obstacle. The most remarkable advantage of this method is that it does not need any prior knowledge about the geometry and physical properties of the scatterer, and requires only the information of the far-field measurements for a finite number of directions of incidence and observation distributed over a limited range. Furthermore, the scheme is very simple and fast since it avoids the use of the iterative procedure and requires only the solution of a linear system. Some numerical examples with synthetic far-field data are given showing the practicality and efficiency of this scheme.

The Fast Acoustic Imaging for Three-Dimensional Scattering Objects in an Oceanic Waveguide

“…As shown in the figure, we obtain quite reasonable images from all six different measurement data. However, imaging becomes worse as the measurement range decreases.This observation is similar to that for alimited aperture imaging in case of the 3D free space [8][9][10][11]. The main reason is that as the measurement aperture decreases, the condition number of the matrix for the linear equation (28) amplifies, hence its ill-posedness intensifies, rendering less numerical precision.…”

“…In practice, however, it is very difficult to obtain prior knowledge of the physical and geometric properties of the objects. In recent years, Yo u&M iao et al [8]- [11] have further introduced an indicator sampling method to overcome these drawbacks.…”

A Qualitative Approach to Inverse Scattering Theory

“…Indeed, having mastered the material in this book, the reader will be fully prepared to understand the literature on qualitative methods for inverse scattering problems arising in other areas of application, such as acoustics and elasticity. In particular, for qualitative methods in the inverse scattering problem for acoustic waves and underwater sound see [12,133,158,159,160], whereas for elasticity we refer the reader to [5,37,38,73,132,135,150].…”

Diffraction of sound by a poroelastic cylindrical absorber near an impedance plane

“…Berntsen [33] addressed the scattering of acoustic waves from an inhomogeneous compactly supported scatterer in a half-space. You and Miao [34] investigated an inverse problem aimed to recover the geometrical characteristics of a three dimensional object in the half-space from the knowledge of the far-field pattern of the acoustic scattering waves. Hasheminejad and Badsar [35] used the novel features of the Biot dynamic model of poroelasticity to present analytical solutions as well as numerical results for general interaction of a plane sound wave with a fluidsaturated poroelastic sphere immersed near the rigid (compliant) boundary of an acoustic half-space.…”