Orthogonal 4-tap integer multiwavelet transforms using matrix factorization

Abstract

An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. Some remarkable properties of orthogonal matrix are presented. Furthermore, the transform matrix is rewritten in a product of two block diagonal matrices and a permutation matrix by the singular value decomposition (SVD) of block recursive matrices. Each block of block diagonal matrices is factorized into triangular elementary reversible matrices (TERMs), which can map integers to integers by rounding arithmetic. Experiment results show that the proposed algorithm is an executable algorithm and outperforms the existing orthogonal 4-tap integer multiwavelet transform algorithm.