1. An image pickup apparatus comprising: an image pickup device including a plurality of pixels arrayed in a two-dimensional form at a predetermined pixel pitch; a pixel shift section configured to perform a pixel shift so that a relative position in a direction of the array in the two-dimensional form between the image pickup device and a light flux received by the image pickup device becomes a plurality of relative positions, which differ in movement amounts, including a relative position in a movement amount which is a non-integral multiple of the pixel pitch; an image pickup control section configured to cause the image pickup device to perform an image pickup operation at the plurality of respective relative positions to acquire a plurality of pieces of image data; an image synthesis section configured to synthesize the plurality of pieces of image data acquired by the image pickup control section, to generate composite image data with a higher resolution than resolution of image data obtained from the image pickup device; and an image processing section configured to determine an edge enhancement parameter based on a characteristic relating to a pixel opening of the composite image data and perform edge enhancement processing for the composite image data using the determined edge enhancement parameter.