1. An image processing device for adding respective mutually corresponding pixels of an original image, including streak artifact, generated from original information and of a smoothed image generated from the same original information and reduced at least in the streak artifact with weighting using a weighting coefficient and generating a target image that an edge of a structure is maintained and the streak artifact is removed, comprising: a function shape determination unit that determines a shape of a nonlinear function on the basis of feature amounts of the original image and the smoothed image; and a weighting coefficient calculation unit that calculates the weighing coefficient on the basis of the nonlinear function, wherein the function shape determination unit includes a division unit that divides regions of the original image and the smoothed image into plural mutually corresponding small regions, a decreasing rate calculation unit that calculates variation values for the small regions pertaining to both of the original image and the smooth image and calculates a decreasing rate of the variation value of the smoothed image based on the variation value of the original image, for each of the small regions, a region extraction unit that extracts a feature amount calculation region from a set of the small regions on the basis of the decreasing rate, and a feature amount calculation unit that calculates the feature amount from a pixel value of the feature amount calculation region.