Inverse problems for three-dimensional localization of an inhomogeneity in a stratified scattering medium by using a weighted Fourier transform

• Characterization of the structure of spatial inhomogeneities embedded in a highly scattering medium is required in many fields. In this paper, a model of a stratified medium embedded with an inhomogeneous ball is considered. With an assumption that the ball is small enough, a perturbation solution to diffusion equation is obtained with some boundary treatments. According to the characteristics of this solution in the two-dimensional Fourier space, a new weighted Fourier transform is used to process the surface data. After this process, a singularity appears at the center of the ball. Combining with the symmetry of the surface data, the information of three-dimensional position of the ball is determined.

Nyckelord

weighted Fourier transform

diffusion equations three-dimensional locating

inhomogeneities

stratified media

diffusion equation

time-domain

tissue

light

reconstruction

transport

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art (ämneskategori)