An digital image input, possibly being either pre-compressed or decompressed, is enhanced; its edges are preserved while any compression artifacts, like blocking and ringing, are simultaneously reduced. The enhancement method enhances images with luminance and chrominance functions, incompletely defined or undefined, on a set of pixels so that the missing information is extrapolated while the image is simultaneously enhanced. The method consists of up to three integrated sub-processes: the image sharpening flow; the de-quantization filtering; and the means of control of the local rate of flow. The image sharpening flow is an iterative nonlinear filtering schema intertwining a local median filter and a suitably chosen linear filter. A local geometric control mechanism allows selective application and adaptation of an algorithm allowing selective removal of local artifacts. De-quantization filtering ensures that the enhancement process does not alter information contained in the image beyond its quantization constraints.