1. An image pickup apparatus comprising: an image pickup for picking up a subject image and outputting image data; an image processor for subjecting the image data that is output from the image pickup to image processing, wherein the image processing includes at least one of an optical shading correction process or a white balance correction process; a synthesizer for synthesizing a plurality of pieces of image data; and a corrector, wherein the image pickup apparatus further includes a controller which performs control in such a manner that the image pickup obtains a plurality of pieces of exposure image data by exposing an image pickup device thereof to light to pick up images, the image processor subjects the plurality of pieces of exposure image data to the image processing, the synthesizer synthesizes the plurality of pieces of exposure image data that are output from the image processor, to generate synthesized exposure image data, the image pickup obtains dark image data by shielding the image pickup device from light to pick up an image, the image processor subjects the dark image data to the image processing using a parameter based on a parameter used in the image processing performed on a corresponding one of the plurality of pieces of exposure image data, and outputs a plurality of pieces of processed dark image data, the synthesizer synthesizes the plurality of pieces of processed dark image data that are output from the image processor, to generate synthesized dark image data, and the corrector corrects the synthesized exposure image data on the basis of the synthesized dark image data.