Stability 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 a general nature and can be used in many applications: in nondestructive evaluation and remote sensing, in geophysical exploration, medical diagnostics, and technology.

[1]  Alexander G. Ramm,et al.  Scattering by obstacles , 1986 .

[2]  Alexander G. Ramm Property C and uniqueness theorems for multidimensional inverse spectral problems , 1990 .

[3]  Alexander G. Ramm,et al.  Multidimensional inverse problems and completeness of the products of solutions to PDE , 1988 .

[4]  Plamen Stefanov Stability of the inverse problem in potential scattering at fixed energy , 1990 .

[5]  Numerical solution of 3d inverse scattering problems with noisy discrete fixed-energy data , 1992 .

[6]  W. Kautz The Approximation Problem , 1954 .

[7]  Patrick Joly,et al.  Mathematical and Numerical Aspects of Wave Propagation Phenomena , 1991 .

[8]  Numerical recovery of the 3D potential from fixed energy incomplete scattering data , 1989 .

[9]  A. Ramm Numerical method for solving 3D inverse problems of geophysics , 1988 .

[10]  M. M. LavrentievJr. An inverse problem for a wave equation , 1991 .

[11]  Rakesh,et al.  Property C and an inverse problem for a hyperbolic equation , 1991 .

[12]  Alexander G. Ramm,et al.  Random fields estimation theory , 1990 .

[13]  L. Hörmander The analysis of linear partial differential operators , 1990 .

[14]  A. Ramm LETTERS TO THE EDITOR: Stability of the numerical method of solving the 3D inverse scattering problem with fixed-energy data , 1990 .

[15]  Completeness of the products of solutions of PDE and inverse problems , 1990 .

[16]  A. G. Ramm,et al.  Recovery of the potential from fixed-energy scattering data , 1988 .

[17]  Alexander G. Ramm,et al.  On completeness of the products of harmonic functions , 1986 .

[18]  Alexander G. Ramm A simple proof of the uniqueness theorem in impedance tomography , 1988 .

[19]  Stability of the solution to inverse scattering problem with exact data , 1992 .

[20]  An inverse problem for Maxwell's equation , 1989 .

[21]  Inverse scattering with fixed-energy data , 1992 .