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The TwoDimensional Lapped Hadamard Transform
Shogo MURAMATSU Akihiko YAMADA Hitoshi KIYA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E81A
No.8
pp.15421549 Publication Date: 1998/08/25 Online ISSN:
DOI: Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing) Category: Keyword: image processing, paraunitary system, symmetric extension, lapped transform, lattice structure,
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Summary:
In this paper, a twodimensional (2D) binaryvalued (BV) lapped transform (LT) is proposed. The proposed LT has basis images which take only BV elements and satisfies the axialsymmetric (AS) property. In one dimension, there is no 2point LT with the symmetric basis vectors, and the property is achieved only with the nonoverlapping basis which the Hadamard transform (HT) has. Hence, in two dimension, there is no 22point separable ASLT, and only 2D HT can be the 22point separable AS orthogonal transform. By taking nonseparable BV basis images, this paper shows that a 22point ASLT can be obtained. Since the proposed LT is similar to HT, it is referred to as the lapped Hadamard transform (LHT). LHT of larger size is shown to be provided with a tree structure. In addition, LHT is shown to be efficiently implemented by a lattice structure.


