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...

A new type of analyzing wavelets which optimally match seismic wavelets (SW wavelets) is presented. It is proved that these wavelets are admissible. The advantages of the SW wavelets are shown for the seismic data processing and attributes analysis. By taking one of the SW wavelets as analyzing wavelet, a wavelet transform method (WT method) of calculating the instantaneous spectrum bandwidth (...

Two-dimensional (2-D) compactly supported, orthogonal wavelets and filter banks having linear phase are presented. Two cases are discussed: wavelets with two-fold symmetry (centrosymmetric) and wavelets with four-fold symmetry that are symmetric (or anti-symmetric) about the vertical and horizontal axes. We show that imposing the requirement of linear phase in the case of order-factorable wavel...