Matrix–valued Wavelets and Multiresolution Analysis
نویسنده
چکیده
We introduce the notions of matrix–valued wavelet set and matrix– valued multiresolution analysis (A-MMRA) associated with a fixed dilation given by an expansive linear map A : R → R, d ≥ 1 such that A(Z) ⊂ Z, in a matrix–valued function space L(R,C), n ≥ 1. These are generalizations of the corresponding notions defined by Xia and Suter in 1996 for the case where d = 1 and A is the dyadic dilation. We show several properties of orthonormal sequences of translates by integers of matrix–valued functions, focusing on those related to the structure of A-MMRA’s and their connection with matrix–valued wavelet sets. Further, we present a strategy for constructing matrix–valued wavelet sets from a given A-MMRA and, in addition, we characterize those matrix–valued wavelet sets which may be built from an A-MMRA.
منابع مشابه
Optimal Interpolatory Wavelets Transform for Multiresolution Triangular Meshes
In recent years, several matrix-valued subdivisions have been proposed for triangular meshes. The matrix-valued subdivisions can simulate and extend the traditional scalar-valued subdivision, such as loop and 3 subdivision. In this paper, we study how to construct the matrix-valued subdivision wavelets, and propose the novel biorthogonal wavelet based on matrix-valued subdivisions on multiresol...
متن کاملConstructions of Vector-Valued Filters and Vector-Valued Wavelets
Let a a1, a2, . . . , am ∈ C be an m-dimensional vector. Then, it can be identified with an m ×m circulant matrix. By using the theory of matrix-valued wavelet analysis Walden and Serroukh, 2002 , we discuss the vector-valued multiresolution analysis. Also, we derive several different designs of finite length of vector-valued filters. The corresponding scaling functions and wavelet functions ar...
متن کاملVector-valued wavelets and vector filter banks
In this paper, we introduce vector-valued multiresolution analysis and vector-valued wavelets for vector-valued signal spaces. We construct vector-valued wavelets by using paraunitary vector lter bank theory. In particular, we construct vector-valued Meyer wavelets that are band-limited. We classify and construct vector-valued wavelets with sampling property. As an application of vector-valued ...
متن کاملOn Multiresolution Methods in Numerical Analysis 4832
As a way to emphasize several distinct features of the mul-tiresolution methods based on wavelets, we describe connections between the multiresolution LU decomposition, multigrid and multiresolution re-duction/homogenization for self-adjoint, strictly elliptic operators. We point out that the multiresolution LU decomposition resembles a direct multigrid method (without W-cycles) and that the al...
متن کامل