Fast inverse solver for magnetic image using time marching scheme with regularization of bounded variations

A computational method for recovering induced magnetic fields due to the existence of cracks are considered. The crack existence can be detected as a sets of magnetic dipoles and the reconstruction of this magnetic charge densities can be done from the magnetic measurement. In practical magnetic measurements, the severe ill-posed problem is caused by the observation noise. The problem is transformed into a well-posed differential-integral equation using output least squares approach with a regularization of bounded variation. A fast computation algorithm is proposed using discrete Fourier transform. Hence the major computational saving can be achieved by applying fast Fourier transform to the convolution in our iterative solver. Experimentally, it has shown the comparison of the computational time for our iterative solver with noise free applying FFT and without FFT.