1. An image pickup apparatus comprising a processor configured of hardware, the processor being configured to function as: a pixel-shift processing section configured to perform pixel shift photographing in a certain focus position to acquire a plurality of image data and perform pixel-shift combination processing of the acquired plurality of image data to generate pixel-shift combined image data; a depth processing section configured to cause the pixel-shift processing section to perform processing on a plurality of focus positions, cause the pixel-shift processing section to generate a plurality of pixel-shift combined image data in different focus positions, and perform depth combination processing of the plurality of pixel-shift combined image data to generate an image having large depth of field; and a focused-region extracting section configured to extract a focused region in at least one of the plurality of focus positions, wherein the pixel-shift processing section performs, concerning a focus position where the focused region is extracted, the pixel-shift combination processing concerning only a partial image region including the focused region.