1. A medical image processing apparatus comprising: a difference calculator configured to receive a plurality of medical image data with different imaging positions and to determine a difference between the plurality of medical image data, so as to generate difference image data that represents the difference; a removal part configured to remove a region corresponding to a structure from the difference image data; a first statistical processor configured to determine a first standard deviation of a pixel value of each pixel of the difference image data with the region corresponding to the structure removed; and an estimation part configured to estimate a second standard deviation of the pixel value of each pixel of the medical image data based on the first standard deviation.