1. An image processing device comprising: an image acquisition unit configured to acquire a mosaic image taken by an imaging unit including an imaging element having a pixel structure of I×J (“I” and “J” are integers of 2 or more, at least one of the integers is 3 or more) pixels in a repeated cycle; a storage unit configured to store each of color mix ratios corresponding to each of pixels in the I×J pixels by being associated with a pixel position in the I×J pixels; a mixed color correction unit configured to eliminate mixed color components mixed from peripheral pixels included in a color signal of each of pixels in the mosaic image acquired by the image acquisition unit, the mixed color correction unit reading out a color mix ratio associated with the pixel position in the I×J pixels of any object pixel for mixed color correction from the storage unit and eliminating the mixed color components included in the object pixel based on the read-out color mix ratio and a color signal of the object pixel; a calculation unit configured to calculate an average value for each color based on a color signal of each of pixels in the mosaic image, in which a mixed color is corrected by the mixed color correction unit; a white balance gain calculation unit configured to calculate a white balance gain based on the average value for each color calculated by the calculation unit; and a white balance correction unit configured to apply white balance correction to the color signal of each of pixels in the mosaic image based on the white balance gain calculated by the white balance gain calculation unit.