Multishot echo-planar imaging is a common strategy in diffusion Magnetic Resonance Imaging to reduce the artifacts caused by the long echo-trains in single-shot acquisitions. However, it suffers from shot-to-shot phase discrepancies associated to subject motion, which can notably degrade the quality of the reconstructed image. Consequently, some type of motion-induced phases error correction needs to be incorporated into the reconstruction process. In this paper we focus on ridig motion induced errors, which have proved to corrupt the shots with linear phase maps. By incorporating this prior knowledge, we propose a maximum likelihood formulation that estimates both the parameters that characterize the linear phase maps and the reconstructed image. In order to make the problem tractable, we follow a greedy iterative procedure that alternates between the estimation of each of them. Simulation data are used to illustrate the performance of the method against state-of-the-art alternatives.