Adaptive Haar transforms with arbitrary time and scale splitting
Karen Egiazarian, Jaakko T. Astola · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2001
The Haar transform is generalized to the case of an arbitrary time and scale splitting. To any binary tree we associate an orthogonal system of Haar-type functions - tree-structured Haar (TSH) functions. Unified fast algorithm for computation of the introduced tree-structured Haar transforms is presented. It requires 2(N - 1) additions and 3N - 2 multiplications, where N is transform order or, equivalently, the number of leaves of the binary tree.