1. An image processing device comprising: a differentiating section which differentiates input image data to generate gradient image data; a gradient domain deconvolution processing section which applies a deconvolution to the gradient image data, the deconvolution performing deblurring corresponding to a prior distribution of an image gradient of an image to generate deconvolved data; and an integrating section which integrates the deconvolved data to generate deblurred image data.