Recent developments in inverse acoustic scattering theory

被引:249
作者
Colton, D [1 ]
Coyle, J
Monk, P
机构
[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA
[2] Univ Strathclyde, Dept Math, Glasgow, Lanark, Scotland
关键词
inverse problems; scattering theory;
D O I
10.1137/S0036144500367337
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We survey some of the highlights of inverse scattering theory as it has developed over the last 15 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.
引用
收藏
页码:369 / 414
页数:46
相关论文
共 79 条
[1]   A distributed source method for inverse acoustic scattering [J].
Angell, TS ;
Jiang, XM ;
Kleinman, RE .
INVERSE PROBLEMS, 1997, 13 (02) :531-545
[2]  
Bers L, 1964, PARTIAL DIFFERENTIAL
[3]  
CARMICHAEL RS, 1982, CRC HDB PHYSICAL PRO
[4]   ON THE INVERSE SCATTERING PROBLEM FOR THE HELMHOLTZ-EQUATION IN ONE DIMENSION [J].
CHEN, Y ;
ROKHLIN, V .
INVERSE PROBLEMS, 1992, 8 (03) :365-391
[5]   UNIQUENESS THEOREMS FOR THE INVERSE PROBLEM OF ACOUSTIC SCATTERING [J].
COLTON, D ;
SLEEMAN, BD .
IMA JOURNAL OF APPLIED MATHEMATICS, 1983, 31 (03) :253-259
[6]   THE NUMERICAL-SOLUTION OF THE 3-DIMENSIONAL INVERSE SCATTERING PROBLEM FOR TIME HARMONIC ACOUSTIC-WAVES [J].
COLTON, D ;
MONK, P .
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1987, 8 (03) :278-291
[7]   A simple method for solving inverse scattering problems in the resonance region [J].
Colton, D ;
Kirsch, A .
INVERSE PROBLEMS, 1996, 12 (04) :383-393
[8]   FAR-FIELD PATTERNS FOR ACOUSTIC-WAVES IN AN INHOMOGENEOUS-MEDIUM [J].
COLTON, D ;
KIRSCH, A ;
PAIVARINTA, L .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (06) :1472-1483
[9]   The inverse electromagnetic scattering problem for an anisotropic medium [J].
Colton, D ;
Potthast, R .
QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 1999, 52 :349-372
[10]   Transmission eigenvalues and a problem of Hans!Lewy [J].
Colton, D ;
Päivärinta, L .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 117 (02) :91-104