1. A method for compressing a compound image, comprising the steps of: forming compound image data into a plurality of blocks; obtaining classifying data that designate one from a plurality of classes for each of a plurality of said blocks, based on predominate compression properties of the block; for each of a plurality of said blocks, obtaining transformed data therefor from either a lossy or a lossless transform selected based on the classifying data for the block; and forwarding that transformed data to one entropy encoder.