1. A method for converting a halftone image having a halftone value for each of a plurality of pixels, into a reconstructed image which for each of said pixels takes on one of more than two possible values, comprising the following steps: representing a halftone image as a plurality of individual pixel values, where each pixel value represents a physical attribute of the image at a corresponding location in the image; for successive individual pixels: defining a set of neighborhood pixels of the individual pixel, the set of neighborhood pixels including the individual pixel and additionally a plurality of pixels proximate said individual pixel; deriving for each pixel of the neighborhood, a significance coefficient that is based upon the value of that pixel, by deriving a baseline value for the individual pixel that is obtained by low pass filtering of the halftone image, and deriving said significance coefficient as a decreasing function f(v) of the absolute difference (v) between the halftone value at the neighborhood pixel and the baseline value for the individual pixel; and deriving the reconstructed value of the individual pixel as a sum over the pixels of the neighborhood of a product of the halftone image value at that neighborhood pixel with the significance coefficient of that neighborhood pixel; and reproducing the image from the reconstructed values of the individual pixels.