Multiresolution decomposition frameworks are instrumental when one needs to focus data analysis at a particular scale or to separate the several contributions to the overall phenomenon, arising from different scales either in time or length. On the other hand, measurement uncertainties are now frequently available along with raw value measurements. In this paper we address the development of mu...

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...

We show that there are no biorthogonal pairs of divergence-free multi-wavelet families on R n , having any regularity, such that both biorthog-onal families have compactly supported, divergence-free generators. This main result generalizes Lemari e's bivariate result. In particular, our method is based on vector-valued multiresolution analyses.

A procedure of the extension of orthogonal multiresolution analysis is introduced by assuming that φ1(x) ia an orthogonal uniscaling function and constructing a new orthogonal multiscaling function Φ(x) = [φ1(x), φ2(x)]. Moreover, an explicit formula of the orthogonal multiwavelets associated with Φ(x) is obtained. Finally, a construction example is given. 2000 Mathematics Subject Classificatio...

Multiresolution analysis plays a major role in wavelet theory. In this paper, multiresolution of Lp spaces is studied. Let S be a shift-invariant subspace of Lp(IR) (1 ≤ p ≤ ∞) generated by a finite number of functions with compact support, and let Sk be the 2-dilate of S for each integer k ∈ ZZ. It is shown that the intersection of Sk (k ∈ ZZ) is always trivial. It is more difficult to deal wi...

Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this ...

A construction of multiscale decompositions relative to domains Ω ⊂ Rd is given. Multiscale spaces are constructed on Ω which retain the important features of univariate multiresolution analysis including local polynomial reproduction and locally supported, stable bases.

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