1. A method for modifying an input digital image having three color channels, each color channel having an (x,y) array of pixel values, to form a modified digital image suitable for use by an inkjet printer using colored and black inks to form a printed image having reduced ink bleed artifacts, comprising: a) computing a transformed digital image responsive to the input digital image, wherein the transformed digital image contains at least a black color channel and a color dependent scale factor channel; b) computing a filtered black color channel from the black color channel using a convolution operation; and c) forming the modified digital image by modifying pixel values in the input digital image in response to the corresponding pixel values of the color dependent scale factor channel and the filtered black color channel, so that when the modified digital image is used to produce a printed image on an inkjet printer there are reduced ink bleed artifacts, wherein the modified digital image has the same three color channels as the input digital image.