Inverse scattering by the stability index method
نویسندگان
چکیده
منابع مشابه
Inverse Scattering by the Stability Index Method
A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which shows how stable the inversion is. If this index is small, then the inversion provides a set of potentials which differ so little, that practically one can re...
متن کاملJour . of Inverse and Ill - Posed Problems , 10 , N 5 , ( 2002 ) INVERSE SCATTERING BY THE STABILITY INDEX METHOD
A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which shows how stable the inversion is. If this index is small, then the inversion provides a set of potentials which differ so little, that practically one can re...
متن کاملStability Estimates in Inverse Scattering
An algorithm is given for calculating the solution to the 3D inverse scattering problem with noisy discrete fixed energy data. The error estimates for the calculated solution are derived. The methods developed are of general nature and can be used in many applications: in nondestructive evaluation and remote sensing, in geophysical exploration, medical diagnostics and technology.
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We show that the enclosure method introduced here is applicable to inverse scattering problems in two dimensions. Using the single set of the Cauchy data of a solution of the Helmholtz equation, we give some formulae for extracting the value of the support functions of unknown sound-hard polygonal obstacles and piecewise linear cracks from the set. AMS: 35R30
متن کاملStability of the numerical method of solving the 3D inverse scattering problem with fixed- energy data
Let IA,(B’B) A(@’, @)I < 6, where 6 > 0 is a small given number, A(@’ , 8 ) is the unknown scattering amplitude at a fixed k > 0 corresponding to a potential q(x)EL2(Bu), q(x) = q(x), q(x) = 0 in a,:= R’\B,, Bo:= {x: 1x1 < a } , @ ‘ , B E S 2 , the unit sphere. Functions qa(x) are constructed, given S z 0 and the function A,(@’ ,@) , such that 11% q/IL2(B,) 4 0 as 6 4 0. The function A,(B’, 0) ...
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ژورنال
عنوان ژورنال: Journal of Inverse and Ill-posed Problems
سال: 2002
ISSN: 1569-3945,0928-0219
DOI: 10.1515/jiip.2002.10.5.487