An algebraic method for inverse source problems and its applications

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We considered the magnetoencephalography inverse problem and proposed a method for estimating the neural current inside the human brain from the magnetic field measured by sensors on a surface that does not encloses the current source. The advantages compared to the conventional methods are that it does not require an initial guess of the solution and iterative computing. Also, for non-destructive inspection of a steel pipe, we proposed two sensors that measure the so-called Fourier coefficients of the magnetic field. Compared to the conventional method using a sensor array, our method can localize a crack on the surface of the pipe by using the two sensors only.