Theory and application of wavelet based bi-orthonormal decomposition method in the solution of linear inverse problems in electromagnetics

Author

Xiaojun Zhu ; Guang-Wen Pan

Author_Institution

Lab. for Signal Propagation, Wisconsin Univ., Milwaukee, WI, USA

Volume

1

fYear

1994

fDate

20-24 June 1994

Firstpage

8

Abstract

A wavelet based bi-orthonormal decomposition method is proposed and applied to the solution of linear inverse problems in electromagnetics. The unknown function is expanded into wavelets, where an adaptive algorithm is developed utilizing the multiresolution properties of the wavelet. The spectral domain method is used to find the bi-orthonormal bases for shift-invariant operators; and the wavelet decomposition method is formulated to construct the biorthonormal bases for general operators. The modified least square QR iterative method is employed to solve the resulting sparse matrix equations. Finally the method is used in the computation of the scattering of TM waves by an elliptic conducting cylinder.<>

Keywords

conductors (electric); electromagnetic wave scattering; inverse problems; iterative methods; least squares approximations; matrix algebra; spectral-domain analysis; wavelet transforms; TM wave scattering; adaptive algorithm; bi-orthonormal bases; bi-orthonormal decomposition method; biorthonormal bases; electromagnetics; elliptic conducting cylinder; general operators; linear inverse problems; modified least square QR iterative method; multiresolution properties; shift-invariant operators; sparse matrix equations; spectral domain method; vaguelettes; wavelet decomposition method; Discrete wavelet transforms; Electromagnetic propagation; Electromagnetic scattering; Integral equations; Inverse problems; Laboratories; Least squares methods; Matrix decomposition; Signal resolution; Singular value decomposition;

fLanguage

English

Publisher

ieee

Conference_Titel

Antennas and Propagation Society International Symposium, 1994. AP-S. Digest

Conference_Location

Seattle, WA, USA

Print_ISBN

0-7803-2009-3

Type

conf

DOI

10.1109/APS.1994.407793

Filename

407793