1. An X-ray imaging apparatus comprising: an X-ray source configured to irradiate X-rays to an object; an X-ray detector configured to obtain a first X-ray image of the object by detecting the X-rays having passed through the object; an image processor configured to perform image processing on the first X-ray image, and to create a second X-ray image; and a display configured to display the second X-ray image, wherein the image processor is configured to generate a noise-reduced image in which a noise is reduced from the first X-ray image, generate a noise image based on differences between the first X-ray image and the noise-reduced image, generate from the noise image, an edge image in which edges are enhanced, combine the noise-reduced image with the edge image to generate the second X-ray image, wherein the image processor is further configured to generate the edge image by multiplying a differential image based on a differentiation for the noise image by a standard deviation image based on a standard deviation for the noise image to generate a first edge filter, and rescaling the first edge filter to generate a second edge filter.