A General Approach for Orthogonal 4-Tap Integer Multiwavelet Transforms. (6th July 2010)

• Record Type: Journal Article
• Authors: Jing, Mingli; Huang, Hua; Liu, Wuling; Qi, Chun
• Other Names: Luongo Angelo Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2010(2010)
• Publication Date: 2010-07-06
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2010/163758
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.