Multivariate Symmetric Interpolating Scaling Vectors with Duals
نویسنده
چکیده
In this paper we introduce an algorithm for the construction of compactly supported interpolating scaling vectors on Rd with certain symmetry properties. In addition, we give an explicit construction method for corresponding symmetric dual scaling vectors and multiwavelets. As the main ingredients of our recipe we derive some implementable conditions for accuracy, symmetry, and biorthogonality of a scaling vector in terms of its mask. Our method is substantiated by several bivariate examples for quincunx and box–spline dilation matrices.
منابع مشابه
Hessian Stochastic Ordering in the Family of multivariate Generalized Hyperbolic Distributions and its Applications
In this paper, random vectors following the multivariate generalized hyperbolic (GH) distribution are compared using the hessian stochastic order. This family includes the classes of symmetric and asymmetric distributions by which different behaviors of kurtosis in skewed and heavy tail data can be captured. By considering some closed convex cones and their duals, we derive some necessary and s...
متن کاملInterpolating Scaling Vectors: Application to Signal and Image Denoising
Interpolating scaling vectors and multiwavelets are particularly attractive for application purposes, because they provide a natural preprocessing procedure. This paper is concerned with the application of the interpolating orthonormal scaling vectors constructed in [10] to signal and image denoising. The results of several wavelets and multiwavelets for both universal and vector thresholding a...
متن کاملNonseparable Orthonormal Interpolating Scaling Vectors
In this paper we introduce an algorithm for the construction of interpolating scaling vectors on Rd with compact support and orthonormal integer translates. Our method is substantiated by constructing several examples of bivariate scaling vectors for quincunx and box– spline dilation matrices. As the main ingredients of our recipe we derive some implementable conditions for accuracy and orthono...
متن کاملAnalysis and Construction of Multivariate Interpolating Refinable Function Vectors
In this paper, we shall introduce and study a family of multivariate interpolating refinable function vectors with some prescribed interpolation property. Such interpolating refinable function vectors are of interest in approximation theory, sampling theorems, and wavelet analysis. In this paper, we characterize a multivariate interpolating refinable function vector in terms of its mask and ana...
متن کاملSymmetric Interpolating Scaling Functions
In many applications, wavelets are usually expected to have the following properties: compact support, orthogonality, linear-phase, regularity, and interpolation. To construct such wavelets, it is crucial designing scaling functions with the above properties. In twoand three-band cases, except for the Haar functions, there exists no scaling function with the above five properties. In -band case...
متن کامل