论文信息 - A Newton-type method for a transmission problem in inverse scattering

A Newton-type method for a transmission problem in inverse scattering

The iteratively regularized Gauss-Newton method is applied to solve an inverse transmission problem for the Helmholtz equation, which is known to be nonlinear and severely ill-posed. We first present a simplified proof of the characterization of the Frechet derivative. Based on this result, we describe an efficient numerical implementation including an error analysis. Finally, we investigate the speed of convergence of the Newton iteration both for exact and for noisy data.

Thorsten Hohage | T. Hohage | C. Schormann | C Schormann

[1] R. Kress. Linear Integral Equations , 1989 .

[2] Rainer Kress,et al. On the numerical solution of a hypersingular integral equation in scattering theory , 1995 .

[3] Rainer Kress,et al. Transmission problems for the Helmholtz equation , 1978 .

[4] Ian H. Sloan,et al. On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation , 1993 .

[5] F. Hettlich. Frechet derivatives in inverse obstacle scattering , 1995 .

[6] Thorsten Hohage,et al. Logarithmic convergence rates of the iteratively regularized Gauss - Newton method for an inverse potential and an inverse scattering problem , 1997 .

[7] Thorsten Hohage,et al. Convergence Rates of a Regularized Newton Method in Sound-Hard Inverse Scattering , 1998 .

[8] A. Bakushinskii. The problem of the convergence of the iteratively regularized Gauss-Newton method , 1992 .

[9] Ralph E. Kleinman,et al. On single integral equations for the transmission problem of acoustics , 1988 .

[10] Roland Potthast,et al. Frechet differentiability of boundary integral operators in inverse acoustic scattering , 1994 .

[11] A. Neubauer,et al. On convergence rates for the Iteratively regularized Gauss-Newton method , 1997 .