Tree-based wavelets for image coding: Orthogonalization and tree selection
In this work we consider the design of the lifting filters and trees used in a separable tree-based wavelet transform. We first consider the use of improved prediction filters, optimized to represent more efficiently smooth signals for arbitrary tree structures. We then consider the design of update filters that are orthogonal to neighboring prediction operators. While the corresponding decomposition is not fully orthogonal, near orthogonality between prediction and update operators leads to significant improvements in energy compaction. Finally we consider the design of trees that (i) avoid filtering across discontinuities in an image to reduce the amount of high frequency energy, while (ii) maintaining some regularity in the downsampled grids over multiple levels of decomposition in order to achieve good spatial localization of filtering.