We propose a method for signal reconstruction in semi-parametric dictionaries. The proposed algorithm estimates both the signal decomposition and the intrinsic parameters of the dictionary during the reconstruction process. Some results about the convergence of the algorithm are presented. The method is used here for the joint reconstruction of a set of misaligned images. Experiments show that the proposed algorithm accurately recovers the set of images and is robust to occlusions and misalignments. This method may have interests in, e.g., non-dynamic cardiac MR imaging where one has access to only subsampled images of the heart at different positions.