Arbitrarily Smooth Orthogonal Nonseparable Wavelets in R
نویسندگان
چکیده
For each r ∈ N, we construct a family of bivariate orthogonal wavelets with compact support that are nonseparable and have vanishing moments of order r or less. The starting point of the construction is a scaling function that satisfies a dilation equation with special coefficients and a special dilation matrix M : the coefficients are aligned along two adjacent rows, and |det(M)| = 2. We prove that if M = ±2I, e. g., M = ( 0 2 1 0 ) or M = ( 1 1 1 −1 ), then the smoothness of the wavelets improves asymptotically by 1 − 1 2 log2 3 ≈ 0.2075 when r is incremented by 1. Hence they can be made arbitrarily smooth by choosing r large enough.
منابع مشابه
A Family of nonseparable Smooth compactly Supported Wavelets
We construct smooth nonseparable compactly supported refinable functions that generate multiresolution analyses on L2(R), d > 1. Using these refinable functions we construct smooth nonseparable compactly supported orthonormal wavelet systems. These systems are nonseparable, in the sense that none of its constituent functions can be expressed as the product of two functions defined on lower dime...
متن کاملProjectable Multivariate Wavelets: Separable vs Nonseparable
Tensor product (separable) multivariate (bi)orthogonal wavelets have been widely used in many applications. On the other hand, non-tensor product (nonseparable) wavelets have been extensively argued in the literature to have many advantages over separable wavelets, for example, more freedom in design of nonseparable wavelets (such design is typically much more complicated and di±cult than the a...
متن کاملConstruction of Trivariate Compactly SupportedBiorthogonal Box Spline
abstract We give a formula for the duals of the mask associated with trivariate box spline functions. We show how to construct trivariate nonseparable compactly supported biorthogonal wavelets associated with box spline functions. The biorthogonal wavelets may have arbitrarily high regularities.
متن کاملConstruction of a class of trivariate nonseparable compactly supported wavelets with special dilation matrix
We present a method for the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -1\1 & 1 & 0 \1 & 0 & 1\end{array}right )$-wavelets under a mild condition. Wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. As an application, an example is provided.
متن کامل