Patient motion is a major limitation for magnetic resonance imaging. Recent theoretical advances incorporate explicit rigid and non-rigid motion compensation into conventional image reconstruction for multi-shot acquisitions and recover motion-free images by solving a general matrix inversion problem. Although the theory has been established, applications are rare due to the challenges of estimating motion field for every pixel of every shot. In this paper we propose a method to overcome this difficulty using the inverse-consistent deformable registration supplying both forward and backward deformations for matrix inversion. We further extend this framework for multi-coil motion compensated image reconstruction using the eigen-mode analysis. Both simulations and in vivo studies demonstrate the effectiveness of our approach.