Wavelets are often characterized through their number of vanishing moments. The more vanishing moments a wavelet has the better are the compaction properties for low-order polynomial signals. However, when bounding wavelets on intervals in order to define wavelet transforms over regions of arbitrary support, some of the moment properties get lost. This is typically accompanied with a loss of co...

Multiwavelet is attracting more and more attention for its good properties such as orthogonality, symmetry, compactly supported, high vanishing moment and balance contrast with the traditional wavelet. These properties, along with optimum time-frequency resolution (OPTFR) are all very important in image processing. Multifilter banks having all properties of symmetry, balancing, optimum time-fre...

In this paper we give a classification of parabolic subalgebras of simple Lie algebras over C that satisfy two properties. The first property is Lynch’s sufficient condition for the vanishing of certain Lie algebra cohomology spaces for generalized Whittaker modules associated with the parabolic subalgebra and the second is that the moment map of the cotangent bundle of the corresponding genera...

∗ Corresponding author. Tel: 86-731-58293939. Supported by a grant from Hunan Education Bureau(09C963). Abstract—Multifilter banks having all properties of symmetry, balancing, optimum time-frequency resolution, arbitrary order vanishing moment, orthogonality and compactly supported together are constructed for the first time. Thus overcome the shortcoming of the present orthogonal optimum time...

In this paper, we study finite element approximations of the viscosity solution of the fully nonlinear Monge-Ampère equation, det(Du) = f (> 0) using the well-known nonconforming Morley element. Our approach is based on the vanishing moment method, which was recently proposed as a constructive way to approximate fully nonlinear second order equations by the author and Feng in [15]. The vanishin...

This paper considers the classical Shannon sampling theorem in multiresolution spaceswith scaling functions as interpolants. As discussed by Xia and Zhang, for an orthogonal scaling function to support such a sampling theorem, the scaling function must be cardinal. They also showed that the only orthogonal scaling function that is both cardinal and of compact support is the Haar function, which...

We introduce a non-linear injective transformation T from the set of non-vanishing normalized Hausdorff moment sequences to the set of normalized Stieltjes moment sequences by the formula T [(an)]n = 1/(a1 · . . . · an). Special cases of this transformation have appeared in various papers on exponential functionals of Lévy processes, partly motivated by mathematical finance. We give several exa...

Recently, the contourlet transform has been developed as a true two-dimensional representation that can capture the geometrical structure in pictorial information. Unlike other transforms that were initially constructed in the continuous-domain and then discretized for sampled data, the contourlet construction starts from the discrete-domain using filter banks, and then convergences to a contin...