1. A machine-implemented method of processing an input image, comprising: computing a forward transform of the input image; applying to the forward transform a bi-selective filter configured to smooth image regions with low magnitude coefficients of the forward transform below a first threshold and to sharpen image regions with high magnitude coefficients of the forward transform above a second threshold, wherein the bi-selective filter is configured to set forward transform coefficient magnitudes below the first threshold to zero, increase forward transform coefficient magnitudes at the second threshold to a first value, increase forward transform coefficient magnitudes above the second threshold to respective values, and to modify forward transform coefficient magnitudes between the first and second thresholds in accordance with a mapping function that increases monotonically with increasing forward transform coefficient magnitude from zero at the first threshold to the first value; and generating an output image from the filtered forward transform.