Recent Developments in Inverse Acoustic Scattering Theory
نویسندگان
چکیده
We survey some of the highlights of inverse scattering theory as it has developed over the past fifteen years, with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves. Included in our presentation are numerical experiments using real data and numerical examples of the use of inverse scattering methods to detect buried objects.
منابع مشابه
Recent Developments in the Qualitative Approach to Inverse Electromagnetic Scattering Theory
We consider the inverse scattering problem of determining both the shape and some of the physical properties of the scattering object from a knowledge of the (measured) electric and magnetic fields due to the scattering of an incident time harmonic electromagnetic wave at fixed frequency. We shall discuss the linear sampling method for solving the inverse scattering problem which does not requi...
متن کاملInverse Acoustic and Electromagnetic Scattering Theory
This paper is a survey of the inverse scattering problem for time-harmonic acoustic and electromagnetic waves at fixed frequency. We begin by a discussion of “weak scattering” and Newton-type methods for solving the inverse scattering problem for acoustic waves, including a brief discussion of Tikhonov’s method for the numerical solution of ill-posed problems. We then proceed to prove a uniquen...
متن کاملInverse scattering theory: renormalization of the Lippmann-Schwinger equation for acoustic scattering in one dimension.
The most robust treatment of the inverse acoustic scattering problem is based on the reversion of the Born-Neumann series solution of the Lippmann-Schwinger equation. An important issue for this approach to inversion is the radius of convergence of the Born-Neumann series for Fredholm integral kernels, and especially for acoustic scattering for which the interaction depends on the square of the...
متن کاملAnalytic continuation of perturbative solutions of acoustic 1D wave equation by means of Padé approximants
The forward scattering series is an important and useful tool in constructing perturbative solutions to wave equation and understanding their relationship to their non-perturbative counterparts. When it converges, the series describes the total wavefield everywhere in a given medium as propagations in a reference medium and interactions with point scatterers. The method can be viewed as constru...
متن کاملInverse scattering without phase information
We report on nonuniqueness, uniqueness and reconstruction results in quantum mechanical and acoustic inverse scattering without phase information. We are motivated by recent and very essential progress in this domain. This paper is an extended version of the talk given at Séminaire Laurent Schwartz on March 31, 2015.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM Review
دوره 42 شماره
صفحات -
تاریخ انتشار 2000