Tree-Structured Haar Transforms

Authors:
Karen Egiazarian;Jaakko Astola
Affiliations:
Signal Processing Laboratory, Tampere University of Technology, P. O. Box 553, FIN-33101, Tampere, Finland karen@cs.tut.fi;Signal Processing Laboratory, Tampere University of Technology, P. O. Box 553, FIN-33101, Tampere, Finland jta@cs.tut.fi
Venue:
Journal of Mathematical Imaging and Vision
Year:
2002

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Abstract

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.