ウェーブレットによるサブバンド分解を利用した散乱逆問題の適切化

概要

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In general, inverse problems related to scientific measurements are ill-posed due to lack of sufficient amount of measured data or due to measurement errors, and an inverse solution is commonly obtained by the minimization procedure for a pertinent functional with various regularization techniques. In this study, a new regularization method based on the sub-band decomposition by orthogonal discrete wavelet transform is proposed for inverse scattering problem. The data representing the distribution of the unknown parameters are decomposed by orthogonal wavelets into components of different spatial scale, and regularization parameters are chosen separately for different components. When some a priori information regarding size and location of the scatterer are available, erroneous components with smaller scale can be damped with higher penalty number while retaining essential information of the scatterers. To demonstrate the validity of the proposed method, the results of the present inverse analysis with wavelet decomposition are compared to those obtained with ordinary inverse analysis for an inverse scattering problem associated with the two-dimensional scalar Helmholtz wave equation linearized by Born approximation.
1998-03-25