1. A method for decomposing a high resolution image into a low resolution replica and supplemental information for facsimile storage or transmission, comprising the steps of: a. obtaining a super pixel, including a plurality of high resolution pixels, from a high resolution image source; b. determining whether a low resolution pixel being generated from said super pixel is at an edge in a low resolution replica being generated, if so, generating supplemental information for said low resolution pixel being generated in accordance with first prescribed criteria dependent on said high resolution pixels in said super pixel and generating said low resolution pixel having a tone determined in accordance with second prescribed criteria, if not, determining whether said low resolution pixel being generated requires supplemental information and, if so, generating supplemental information for said low resolution pixel being generated in accordance with said first prescribed criteria and selecting the tone of said low resolution pixel being generated so that it is at an edge in said low resolution replica and, if not, generating said low resolution pixel having a tone determined in accordance with third prescribed criteria; c. outputting said supplemental information, if any; d. outputting a representation of said generated low resolution pixel tone; e. obtaining a next super pixel from said high resolution image source as in step (a); f. repeating steps (b) through (e) until the high resolution image has been decomposed to a low resolution replica plus supplemental information, if any.