Resolution Scalable Lossless Progressive Image Coding via Conditional Quadrisection

Given a square image with number of rows and columns a power of two, we obtain an image sequence by continued downsampling by a factor of two until only a single pixel remains. We use each downsampled image as context for lossless coding of the next image in the sequence. The image coder makes use of a grammar called the conditional quadrisection grammar for building the next image given the context image; the production rules of the conditional quadrisection grammar are encoded via a simple arithmetic encoding technique. We present a universal coding theorem establishing that the redundancy/pixel of our scheme with respect to finite-state resolution scalable lossless image coding schemes tends to zero as the size of the image grows without bound. We present the results of compression experiments in which our scheme is evaluated on real images.