1. An image processing apparatus for processing an image obtained by fluoroscopying a subject, the image processing apparatus includes: (A) a device configured to generate a band image by extracting a part of frequency components in an original image with a figure of the subject appearing therein; (B) a device configured to calculate magnitude and a direction of gradient of a pixel value for each pixel of the band image; (C) an isotropic blurring device configured to generate an isotropic blur image by applying an isotropic smoothing filter to the band image; (D) an anisotropic blurring device configured to generate an anisotropic blur image by applying an anisotropic smoothing filter to the band image, the anisotropic smoothing filter depending on the direction of the gradient; (E) a device configured to calculate an index for the each pixel in accordance with the magnitude of the gradient and pixel values surrounding the pixel in the band image; and (F) a processed image generating device configured to superimpose the band image, the isotropic blur image, and the anisotropic blur image for the each pixel with weighting based on the index, thereby generating a processed image with a noise component removed from the original image.