1. An MRI apparatus comprising: an MR signal acquiring device for acquiring MR signals; a window-processing device for window-processing the MR signals using a window function that has a value less than one at a center and in its proximate region in a k-space and on a periphery and in its proximate region in the k-space, and, between the regions in which the window function has a value less than one, has a value larger than that in the regions in which the window function has a value less than one; and a Fourier-transformation processing device for applying Fourier-transformation processing to the window-processed MR signals to obtain an MR image.