Reversible Factorization of U Orthogonal Transform and Image Lossless Coding

U orthogonal transform is applied into the image lossless coding, and the factorizations of U orthogonal matrices into triangular elementary reversible matrices (TERMs) and single-row elementary reversible matrices (SERMs) are investigated. The TERM factorization of an N by N matrix is determined by N-1 free variables, and therefore, the local approximate optimal TERM factorization can be found by shrinking search-interval of the N-1 free variables. If row exchange is used, an 8×8 orthogonal matrix has only 40320 forms of SERM factorizations, and the approximate optimal SERM factorization can be found with the exhaustion search algorithm. At the end, image lossless coding is achieved by using reversible U matrices, and the experimental results show that the code-rate of lossless compression based on reversible U transform is comparable to that of near lossless compression based on float U orthogonal transform; the coding efficiency of SERM factorization outperforms that of TERM; the image coding performance of U orthogonal transform of degree 3 is approximate to that of DCT. As a result, the U orthogonal transformation of degree 3 can be used into the image lossless coding instead of DCT.