Abstract: A method of and system for rendering a halftone image of a gray scale image by utilizing a pixel-by-pixel comparison of the gray scale image against a blue noise mask is disclosed in which the gray scale image is scanned on a pixel-by-pixel basis and compared on a pixel-by-pixel basis to an array of corresponding data points contained in a blue noise mask stored in a PROM or computer memory in order to produce the desired halftoned image. Both digital and optically implemented halftone methods are disclosed. A method for obtaining the inverse halftone or gray scale image of a halftone image is also disclosed in which the halftone image can be comprised of clustered dots or dispersed dots, and it is not necessary to have knowledge of the screening methods or parameter. A method for transmitting and receiving a gray scale image in a compressed and decompressed manner, respectively, is disclosed for efficient facsimile transmission of images.