1. An image processing device which comprises image processing means for, while conserving the edges with the pixel values which change abruptly out of input image data, amplifying the portions other than said edges, said image processing means comprising: smoothing means for smoothing said input image data while conserving said edges of said input image data and for generating smoothed image data; and image enhancing means for subtracting said smoothed image data from said input image data, for amplifying the subtraction result and then adding said smoothed image data, and for generating output image data, and further said smoothing means comprising: nonlinear converting means for performing nonlinear conversion on each of said input image data and generating nonlinear image data; nonlinear filtering means for applying nonlinear digital filter to said nonlinear image data and generating nonlinear smoothed image data; and nonlinear inverting means for performing inversion of said nonlinear converting means on said nonlinear smoothed image data and generating smoothed image data.