Open AccessA General Approach for Orthogonal 4-Tap Integer Multiwavelet Transforms
Author(s) -
Mingli Jing,
Hua Huang,
Wuling Liu,
Chun Qi
Publication year - 2010
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2010/163758
Subject(s) - mathematics , integer (computer science) , singular value decomposition , orthogonal matrix , matrix (chemical analysis) , block matrix , permutation matrix , algorithm , block (permutation group theory) , rounding , matrix decomposition , integer matrix , combinatorics , discrete mathematics , orthogonal basis , nonnegative matrix , symmetric matrix , computer science , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , circulant matrix , composite material , programming language , operating system
An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition (SVD) of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermore, we factorize the block matrix of block diagonal matrices into triangular elementary reversible matrices (TERMs), which map integers to integers by rounding arithmetic. The cost of factorizing block matrix into TERMs does not increase with the increase of the dimension of transform matrix, and the proposed algorithm is in-place calculation and without allocating auxiliary memory. Examples of integer multiwavelet transform using DGHM and CL are given, which verify that the proposed algorithm is an executable algorithm and outperforms the existing algorithm for orthogonal 4-tap integer multiwavelet transform
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