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Comparison of the born iterative method and tarantola's method for an electromagnetic time‐domain inverse problem
Author(s) -
Moghaddam M.,
Chew W. C.,
Oristaglio M.
Publication year - 1991
Publication title -
international journal of imaging systems and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.359
H-Index - 47
eISSN - 1098-1098
pISSN - 0899-9457
DOI - 10.1002/ima.1850030405
Subject(s) - iterative method , inverse problem , mathematics , mathematical optimization , nonlinear system , optimization problem , integral equation , computer science , inverse scattering problem , algorithm , mathematical analysis , physics , quantum mechanics
Two methods of solving the nonlinear two‐dimensional electromagnetic inverse scattering problem in the time domain are considered. These are the Born iterative method and the method originally proposed by Tarantola for the seismic reflection inverse problems. The former is based on Born‐type iterations on an integral equation, whereby at each iteration the problem is linearized, and its solution is found via a regularized optimization. The latter also uses an iterative method to solve the nonlinear system of equations. Although it linearizes the problem at each stage as well, no optimization is carried out at each iteration; rather the problem as a whole is posed as a (regularized) optimization. Each method is described briefly and its computational complexity is analyzed. Tarantola's method is shown to have a lower numerical complexity compared to the Born iterative method for each iteration, but in the examples considered, required more iterations to converge. Both methods perform well when inverting a smooth profile; however, the Born iterative method gave better results in resolving localized point scatterers.