Joint Optimization of Scalar and Tree-structured Quantization of Wavelet Image Decompositions

Wavelet image decompositions generate a tree-structured set of coeecients, providing an hierarchical data-structure for representing images. While early wavelet-based algorithms for image compression concentrated on optimal quantization of wavelet coee-cients, several recent researchers have proposed approaches which couple coeecient quantization (either scalar or vector-based) with various strategies for quantizing the tree itself. This paper proposes an image compression algorithm based on optimal bit rate allocation between scalar and tree-structured quantiz-ers. A predictive approach to representing the pruned tree structure is presented, and the entropy of this representation is included in the optimal allocation problem. The algorithm couples Lagrangian optimization of scalar quantizers with a marginal analysis approach for optimizing the tree structure, and achieves excellent coding eeciency in the rate-distortion sense.