1. A method for sharpening an original digital image comprising: generating a smoothed image from the original image; generating a residual image from the smoothed image and the original image by generating the ratio between the original image and the smoothed image, then for positive values of the difference between the rational residual image and one, multiplying the difference between the residual image values and one by a factor and adding the product to one, and for negative values of the difference between the rational residual image and one, multiplying the difference between the inverse residual image values and one by the factor, adding the product to one and dividing one by the sum; generating a sharpened smoothed image; and combining the residual image and the sharpened smoothed image to produce a sharpened version of the original image.