1. An image capturing apparatus, comprising: an image capturing unit configured to capture an image by exposure for a first exposure time to generate a short-time exposure image, and an image by exposure for a second exposure time to generate a long-time exposure image, the second exposure time being longer than the first exposure time; a short-time exposure image storage unit configured to store the short-time exposure image generated by said image capturing unit; a long-time exposure image storage unit configured to store the long-time exposure image generated by said image capturing unit; a motion blur adding unit configured to generate a predicted image of the long-time exposure image, the predicted image being an image generated by adding motion blur to the short-time exposure image stored in said short-time exposure image storage unit; a subtracting unit configured to calculate a difference between the long-time exposure image stored in said long-time exposure image storage unit and the predicted image generated by said motion blur adding unit to generate a difference image; and a coding unit configured to code the short-time exposure image stored in said short-time exposure image storage unit and the difference image generated by said subtracting unit.