Reconstruction of the photon diffusion coefficient in optical tomography

In this paper, we consider the recovery of photon diffusion coefficient in the case of piecewise constant coefficients in optical tomography from boundary measurements of light propagation within a tissue. We propose an effective reconstruction algorithm to detect the number, the location, the size and the shape of piecewise constant coefficients. This problem is nonlinear and severely ill-posed, thus we should consider a regularisation technique in our approach in order to improve the corresponding approximation. We give several examples to show the viability of our proposed method.