We propose a partial occlusion removal method for computational integral imaging reconstruction (CIIR) based on the usage of the exemplar based inpainting technique. The proposed method is an improved version of the original linear inpainting based CIIR (LI-CIIR), which uses the inpainting technique to fill in the data missing region. The LI-CIIR shows good results for images which contain objects with smooth surfaces. However, if the object has a textured surface, the result of the LI-CIIR deteriorates, since the linear inpainting cannot recover the textured data in the data missing region well. In this work, we utilize the exemplar based inpainting to fill in the textured data in the data missing region. We call the proposed method the neighboring elemental image exemplar based inpainting (NEI-exemplar inpainting) method, since it uses sources from neighboring elemental images to fill in the data missing region. Furthermore, we also propose an automatic occluding region extraction method based on the use of the mutual constraint using depth estimation (MC-DE) and the level set based bimodal segmentation. Experimental results show the validity of the proposed system.