The planar compound eye imaging system uses multiple sub-apertures to image the scene. Due to the constraint of the imaging sub-aperture size and spatial sampling rate of the image sensor, the image quality of each sub-aperture is low. How to fuse multiple sub-aperture images for a high-resolution image is an urgent problem. Multi-image super-resolution theory uses multiple images with complementary information to reconstruct high spatial resolution image. However, existing theories usually adopt the oversimplified motion model which is not suitable for planar compound eye imaging. If the existing multi-image super-resolution theory is directly applied to the resolution enhancement of the planar compound eye, the inaccurate motion estimation will reduce the performance of image resolution enhancement. In order to solve these problems, the motion model of the multi-image super-resolution is improved in the variational Bayesian framework, and the derived joint estimation algorithm is used to enhance the resolution of the planar compound eye. The correctness and effectiveness of the proposed method is verified by the simulation data experiments and the real compound eye data experiments.