Wavelet solution of the inverse source problems

Generally, the inverse source problem is reduced into solving an ill-posed system of equations. This article proposes a novel approach for the inverse source problem employing the wavelet analysis. The wavelet analysis has two distinguished abilities; one is the image data compression ability and the other is the spectrum resolution ability of the waveforms. The key idea is that the system matrix of the inverse source problems is regarded as a two-dimensional image data. The two-dimensional wavelet transform is applied to this system matrix. Finally, we can obtain an approximate inverse matrix of the system. A simple example concerning the estimation of the current distribution from the locally measured magnetic fields demonstrates the validity of our approach.