Symmetric multivariate orthogonal refinable functions
نویسندگان
چکیده
منابع مشابه
Symmetric Multivariate Orthogonal Refinable Functions
In this paper, we shall investigate the symmetry property of a multivariate orthogonal M -refinable function with a general dilation matrix M . For an orthogonal M -refinable function φ such that φ is symmetric about a point (centro-symmetric) and φ provides approximation order k, we show that φ must be an orthogonal M -refinable function that generates a generalized coiflet of order k. Next, w...
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A biorthogonal wavelet is derived from a pair of biorthogonal refinable functions using the standard technique in multiresolution analysis. In this paper, we introduce the concept of projectable refinable functions and demonstrate that many multivariate refinable functions are projectable; that is, they essentially carry the tensor product (separable) structure though themselves may be non-tens...
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Abstract. The paper develops a necessary condition for the regularity of a multivariate refinable function in terms of a factorization property of the associated subdivision mask. The extension to arbitrary isotropic dilation matrices necessitates the introduction of the concepts of restricted and renormalized convergence of a subdivision scheme as well as the notion of subconvergence, i.e., th...
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This paper characterizes the stability and orthonormality of the shifts of a multidimensional (M; c) reenable function in terms of the eigenvalues and eigenvectors of the transition operator W cau deened by the autocorrelation c au of its reenement mask c; where M is an arbitrary dilation matrix. Another consequence is that if the shifts of form a Riesz basis, then W cau has a unique eigenvecto...
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Smoothness and symmetry are two important properties of a refinable function. It is known that the Sobolev smoothness exponent of a refinable function can be estimated by computing the spectral radius of a certain finite matrix which is generated from a mask. However, the increase of dimension and the support of a mask tremendously increases the size of the matrix and therefore makes the comput...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2004
ISSN: 1063-5203
DOI: 10.1016/j.acha.2003.12.004