New continuous wavelets of compact support are introduced, which are related to the beta distribution. They can be built from probability distributions using ”blur”derivatives. These new wavelets have just one cycle, so they are termed unicycle wavelets. They can be viewed as a soft variety of Haar wavelets whose shape is fine-tuned by two parameters a and b. Close expressions for beta wavelets...

Previously, the use of non-separable wavelets in image processing has been hindered by the lack of a fast algorithm to perform a non-separable wavelet transform. We present two such algorithms in this paper. The rst algorithm implements a periodic wavelet transform for any valid wavelet lter sequence and dilation matrices satisfying a trace condition. We discuss some of the complicating issues ...

In this paper, we describe an algorithm for computing biorthogonal compactly supported dyadic wavelets related to the Walsh functions on the positive half-line R+. It is noted that a similar technique can be applied in very general situations, e.g., in the case of Cantor and Vilenkin groups. Using the feedback-based approach, some numerical experiments comparing orthogonal and biorthogonal dyad...

In this paper we systematically define Haar-like wavelets over a tetrahedrical grid which is generated b y a regular subdivision method. These wavelets form an inconditional basis for LJ'(T,C,p), 1 < p < 00 , being p the Lebesgue measure and C the U-algebra of all tetrahedra generated from a tetrahedron T by the chosen subdivision method.

The coefficients of a wavelet–decomposition form into different levels according to the size of the described details. This can be utilized to crypt only a part of the given data while keeping the rest unchanged so that critical information is filtered out. I achieved this idea with Haar–wavelets for a special type of data and show in addition an a priori error estimation.

in this paper, we present a numerical method for solving nonlinear fredholm and volterra integral equations of the second kind which is based on the use of haar wavelets and collocation method. we use properties of block pulse functions (bpf) for solving volterra integral equation. numerical examples show efficiency of the method.

We construct piecewise constant wavelets on spherical triangulations, which are orthogonal with respect to a scalar product on L(S), defined in [3]. Our classes of wavelets include the wavelets obtained by Bonneau in [1] and by Nielson et all. in [2]. We also proved the Riesz stability and showed some numerical experiments.