The Two-Dimensional Lapped Hadamard Transform

Shogo MURAMATSU  Akihiko YAMADA  Hitoshi KIYA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E81-A    No.8    pp.1542-1549
Publication Date: 1998/08/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing)
image processing,  paraunitary system,  symmetric extension,  lapped transform,  lattice structure,  

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In this paper, a two-dimensional (2-D) binary-valued (BV) lapped transform (LT) is proposed. The proposed LT has basis images which take only BV elements and satisfies the axial-symmetric (AS) property. In one dimension, there is no 2-point LT with the symmetric basis vectors, and the property is achieved only with the non-overlapping basis which the Hadamard transform (HT) has. Hence, in two dimension, there is no 22-point separable ASLT, and only 2-D HT can be the 22-point separable AS orthogonal transform. By taking non-separable BV basis images, this paper shows that a 22-point 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.