1. An X-ray CT apparatus comprising: an X-ray source that generates X-rays; an X-ray detector that is disposed opposite the X-ray source and detects the X-ray transmitted through an object to output projection data of the object; rotation means configured to rotate the X-ray source and the X-ray detector in a state where the X-ray source and the X-ray detector are disposed opposite each other; filter generation means configured to generate an image processing filter that changes according to feature amounts of a pixel value included in the projection data; reconstruction means configured to generate an X-ray CT image of the object by performing a reconstruction operation on the projection data using the generated image processing filter; and image display means configured to display the X-ray CT image.