In recent years, researchers have obtained impressive reconstructions of the refractive index (RI) of biological objects through the combined use of advanced physics (nonlinear forward model) and regularization. Here, we propose an adaptation of these techniques for the more challenging problem of intensity-only measurements. It involves a difficult nonconvex optimization problem where phase and distribution of the RI must be jointly estimated. Using an adequate splitting, we leverage recent achievements in phase retrieval and RI reconstruction to perform this task. This yields an efficient reconstruction method with sparsity constraints.