Recovery of inclusions in 2D and 3D domains for Poisson's equation

In this paper, we consider the recovery problem of inclusions in three-dimensional and three-dimensional domains for Poisson's equation from noisy observation data. We propose effective reconstruction algorithms to recover hidden inclusions within a body when one can only make measurements of voltage and current on the external boundary. Our motivation is to detect the number, the location, the size and the shape of inclusions. This problem is nonlinear and severely ill posed, thus we should apply regularization techniques in our approaches in order to improve the corresponding approximation. We give several examples to show the viability of our proposed methods.