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—Reversible integer mapping is essential for lossless source coding by transformation. A general matrix factorization theory for reversible integer mapping of invertible linear transforms is developed in this paper. Concepts of the integer factor and the elementary reversible matrix (ERM) for integer mapping are introduced, and two forms of ERM—triangular… (More)

This paper presents an algebraic approach to construct M-band orthonormal wavelet bases with perfect reconstruction. We first derive the system of constraint equations of M-band filter banks, and then an algebraic solution based on matrix decomposition is developed. The structure of the solutions is presented, and practical construction procedures are… (More)

In this paper, an image denoising operator deened b y a non-linear partial diierential equationPDE is presented. Similar to the operators proposed by Perona, Malik and Catt e et al., it can remove noise, enhance step-like edges and keep the locality of the edges. Its extra ability is to keep thin edges. The criterion for stopping time is also investigated.… (More)

This paper presents an algebraic approach to construct M-band orthogonal wavelet bases. A system of constraint equations is obtained for M-band orthonormal filters, and then a solution based on SVD (Singular Value Decomposition) is developed to enable us to produce innumerable wavelet bases of given length. Also the property of 2 vanishing moments is… (More)

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