Diffuse Optical Tomography (DOT) is a noninvasive medical imaging technique to probe highly heterogeneous turbid media based on measurements of near-infrared light on the boundary of the material. Since the inverse problem in DOT is nonlinear and severely ill-posed, only low resolution reconstructions are feasible nowadays when noise is added to the data. Therefore, we present individual and simultaneous
imaging reconstructions of the absorption and scattering coefficients using the Levenberg-Marquardt-Kaczmarz (LMK) method and its improved loping-LMK method with sparsity and total variation regularizations, modelling the propagation of the light with the time-dependant radiative transfer equation (RTE) in two dimensions. In addition, an individual and simultaneous contrast value and shape reconstructions are presented using the level set method.