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...

background : ruptured cerebral aneurysms (icas) are the most common non-traumatic cause of subarachnoid hemorrhage (sah) that is associated with life threatening complications such as vasospasm, infarction, and hydrocephalus (hcp). the active participation of macrophage/monocyte-mediated inflammatory response in the pathogenesis of cerebral aneurysm as labeled with monocyte chemoattractantprote...

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...

This is part of a program devoted to the study of wavelets by making use of their Fourier transforms. We shall rst give a constructive characterization of all minimally-supported-frequencies(m.s.f.) wavelets. Then we use this to construct new m.s.f. wavelets, including ones that are not band-limited. We shall also provide a simple necessary and suucient condition for an m.s.f. wavelet to be ass...