1. A signal-processing system comprising: a processing component for executing signal processing instructions; and a signal-processing routine executed by the processing component that receives pixel data presenting a digital image and outputs pixel data representing a sharpened version of the digital image, wherein the signal-processing routine, at each of one or more currently considered scales of resolution greater than a lowest resolution scale, processes an input signal to produce an output signal by downscaling either the input signal or a first internal signal derived from the input signal to produce a next input signal for a next-lower resolution scale, upscaling a second internal signal received from a lower-resolution scale to produce a first intermediate signal from which the output signal to a next-higher-resolution scale is produced, and robustly filtering at least one of the input signal and the first intermediate signal by differencing each pixel in the image with a plurality of surrounding pixels and using those differences to identify corresponding values of a non-linear function, the combination of which provides a value for a corresponding pixel in a robustly filtered version of the image; wherein said robustly filtering further comprises a function to remove any new local maxima and minima introduced by the robust filtering.