1. A method of sharpening a digital image having image pixels according to its material content, comprising the steps of: a) generating a subject matter belief map corresponding spatially to the image pixels, having belief values indicating the likelihood that respective image pixels are representative of a particular subject matter; b) generating a noisy pixel belief map corresponding spatially to the image pixels having belief values indicating the likelihood that the modulation about respective pixels are due to system noise; c) generating gain map from the subject matter belief map and the noisy pixel belief map having gain values that indicate the degree of sharpening to be applied to the image pixels; and d) using the gain map to sharpen the image.