Conventional Cone Beam CT (CBCT) is composed of a single source and a large detector to aquire a full sinogram of the object. Multi-source inverse geometry CT system (IGCT) consists, for its part in using several sources and a small detector to acquire several partial sinograms of the object. For technological, financial and medical reasons the reduction of the number of sources and the reduction of the detector size are interesting but induce to solve an ill-posed and ill-conditionned problem. We propose a regularized iterative algorithm which is able to reconstruct the object volume from partial sinograms acquired with a an optimized multi-source IGCT system : we will demonstrate the performance of the proposed algorithm when we reduce the size of the detector and the number of sources. Realistically simulated CT data is reconstructed with the proposed algorithm and the results are compared to those obtained by filtered backprojection (FBP) and those obtained by a maximum likelihood estimation to show the impact of the regularization.