Adaptive transforms for image coding using spatially varying wavelet packets

We introduce a novel, adaptive image representation using spatially varying wavelet packets (WP’s). Our adaptive representation uses the fast double-tree algorithm introduced in [l] to optimize an operational rate-distortion (R-D) cost function, as is appropriate for the lossy image compression framework. This involves jointly determining which filter hank tree (WP frequency decomposition) to use, and when to change the filter hank tree (spatial segmentation). For optimality, the spatial and frequency segmentations must be done jointly, not sequentially. Due to computational complexity constraints, we consider quadtree spatial segmentations and binary WP frequency decompositions (corresponding to two-channel filter hanks) for application to image coding. We present results verifying the usefulness and versatility of this adaptive representation for image coding using both a first-order entropy rate-measure-based coder as well as a powerful space-frequency quantization-based (SFQ-based) wavelet coder introduced in [ll].