1. A pixel interpolating device comprising: a cycle calculation unit that calculates a cycle in change of pixel values of pixels in a document image obtained by reading a document by first and second photoelectric conversion element arrays each having a plurality of photoelectric conversion elements; and an interpolating unit that extracts from the pixels such pixels that a distance between each pixel and an interpolated pixel corresponding to a position between the first and second photoelectric conversion element arrays corresponds to the cycle calculated by the cycle calculation unit, and that interpolates a pixel value of the interpolated pixel based on pixel values of the extracted pixels.