This paper deals with the design of interpolating wavelets based on a variety of Lagrange functions, combined with novel signal processing techniques for digital imaging. Halfband Lagrange wavelets, B-spline Lagrange wavelets and Gaussian Lagrange (Lagrange distributed approximating functional (DAF)) wavelets are presented as specific examples of the generalized Lagrange wavelets. Our approach ...

In this paper we construct IR n-valued biorthogonal, compactly supported multiwavelet families such that one of the biorthogo-nal pairs consists of divergence-free vector wavelets. The construction is based largely on Lemari e's idea of multiresolution analyses intertwined by diierentiation. We show that this technique extends nontrivially to multiwavelets via Strela's two-scale transform. An e...

Abstract: Wavelet transformation is a new development in the area of applied mathematics. Wavelets are mathematical tools that cut data or functions or operators into different frequency components, and then study each component with a resolution matching to its scale. In this article, we have made a brief discussion on historical development of wavelets, basic definitions, formulations of wave...

In a previous paper we constructed some Haar wavelets on spherical triangulations, which are orthogonal with respect to a weighted inner product on L2(S2). We obtained two classes of wavelets which included certain wavelets obtained by Bonneau and Nielson et al. Each of these classes depended on two parameters which satisfied a relation. In this paper we study which of these wavelets are optima...

This paper offers a new regard on compactly supported wavelets derived from FIR filters. Although being continuous wavelets, analytical formulation are lacking for such wavelets. Close approximations for daublets (Daubechies wavelets) and their spectra are introduced here. The frequency detection properties of daublets are investigated through scalograms derived from these new analytical expres...

Since wavelets were introduced in the radiosity algorithm5, surprisingly little research has been devoted to higher order wavelets and their use in radiosity algorithms. A previous study13 has shown that wavelet radiosity, and especially higher order wavelet radiosity was not bringing significant improvements over hierarchical radiosity and was having a very important extra memory cost, thus pr...

In this paper we construct certain continuous piecewise rational wavelets on arbitrary spherical triangulations, giving explicit expressions of these wavelets. Our wavelets have small support, a fact which is very important in working with large amounts of data, since the algorithms for decomposition, compression and reconstruction deal with sparse matrices. We also give a quasi-interpolant ass...

Discrete autocorrelation wavelets have recently been applied in the statistical analysis of locally stationary time series. This form of time series analysis also requires the construction of the inner product matrix of such wavelets. To date, both discrete autocorrelation wavelets and the inner product matrix have been constructed via a brute force technique which proves to be computationally ...

In this paper, we study the problem of constructing non-separable band-limited wavelet tight frames, Riesz wavelets and orthonormal wavelets in R and R. We first construct a class of non-separable band-limited refinable functions in low-dimensional Euclidean spaces by using univariate Meyer’s refinable functions along multiple directions defined by classic box-spline direction matrices. These n...