Constrained wavelet packets for tree-structured video coding algorithms

Traditional wavelet packet (WP) optimization techniques neglect information about the structure of the lossy part of the compression scheme. Such information, however, can help guide the optimization procedure so as to result in efficient WP structures. We propose a wavelet packet algorithm with a constrained rate-distortion optimization which makes it suited to subsequent tree-structured coding such as with the set partitioning in hierarchical trees (SPMT) algorithm. The (octave-band) wavelet transform lends itself to simple and coherent tree-shaped spatial relations which can then be used to define zero-trees. Yet, input images have different frequency distributions and an adaptive transform such as WP is bound to be more efficient on an image-by-image basis. With WP algorithms, the coefficients in the WP domain can be rearranged to produce what resembles (or simulates) the normal wavelet transform structure. This stage is usually performed to simplify the coding stage. However, an unconstrained optimization can result in a transformed image with complicated or incoherent tree-shaped spatial relations. This work aims to show that the efficiency of embedded coders such as SPMT and Shapiro's Zerotrees strongly depends on WP structures with coherent spatial tree relationships.