Inverse Analysis of Magnetic Fields by Using the Wavelets
Tatsuya Doi, Seiji Hayano, Yoshifuru SAITO · IEEJ Transactions on Fundamentals and Materials · 1997
The inverse problems are classified into two major categories, i. e. one is the inverse parameter problem; the other is the inverse source problem. Generally, the inverse problems are reduced into solving an ill-posed system of equations. This article proposes a novel approach for the inverse problems employing the wavelet analysis. Key idea is that the system matrix of the inverse problems is regarded as two-dimensional signal data. The two-dimensional wavelet transform is applied to this system matrix. Finally, an approximate inverse matrix of the system is obtained. We apply our approach to examples of both the inverse source and parameter problems. Simple examples demonstrate the validity of our approach.