The derivatives of the Gaussian function, G(x) = 1 √ 2π e−x 2/2, produce the Hermite polynomials by the relation, (−1)mG(m)(x) = Hm(x)G(x), m = 0, 1, . . . , where Hm(x) are Hermite polynomials of degree m. The orthonormal property of the Hermite polynomials, 1 m! ∫∞ −∞Hm(x)Hn(x)G(x)dx = δmn, can be considered as a biorthogonal relation between the derivatives of the Gaussian, {(−1)nG(n) : n = ...

the construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. we apply this system as basis functions to solve the fractional differential and integro-differential equations. biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. some test pr...

In this paper, we present the estimation of Poisson intensity based on hypothesis testing in the wavelet domain for any dimensional data. The testing framework for wavelet-based Poisson intensity estimation was first introduced by Kolaczyk, where a thresholding estimator, which realizes the hypothesis testing, is derived for Haar wavelet coefficients. Here we propose for the same wavelet a new ...

Iris recognition has been demonstrated to be an efficient technology for doing personal identification. In this work, a method to perform iris recognition using biorthogonal wavelets is introduced. Effective use of biorthogonal wavelets using a lifting technique to encode the iris information is demonstrated. This new method minimizes built in noise of iris images using in-band thresholding in ...

The existence in L2(R) of biorthogonal wavelet bases associated with perfect reconstruction 2 channel filter banks comprising finite, real filters is determined by the eigenvalues of two related Lawton matrices. Each Lawton matrix is required to have a simple eigenvalue at one and all remaining eigenvalues must have modulus less than one. This being the case then the wavelet bases are said to b...

We present a new family of compactly supported and symmetric biorthogonal wavelet systems. Each refinement mask in this family has tension parameter ω. When ω = 0, it becomes the minimal length biorthogonal Coifman wavelet system [22]. Choosing ω away from zero, we can get better smoothness of the refinable functions at the expense of slightly larger support. Though the construction of the new ...

We present a scheme that leverage orthonormal or biorthogonal wavelets to a new system of biorthogonal wavelets. The leveraged biorthogonal wavelets will have some nice properties. If we start with orthonormal wavelets, the leveraged scaling functions and wavelets are compactly supported and are diierentiable. The derivatives of the leveraged wavelets are orthogonal to their translations; the d...

We present a scheme that leverage orthonormal or biorthogonal wavelets to a new system of biorthogonal wavelets. The leveraged biorthogonal wavelets will have some nice properties. If we start with orthonormal wavelets, the leveraged scaling functions and wavelets are compactly supported and are diierentiable. The derivatives of the leveraged wavelets are orthogonal to their translations; the d...

This paper is concerned with developing conditions on a given nite collection of compactly supported algebraically linearly independent reenable functions that insure the existence of biorthog-onal systems of reenable functions with similar properties. In particular we address the close connection of this issue with stationary subdivision schemes. 1 Introduction During the past few years the co...

In this article, we present a constructive technic of biorthogonal nonstationary wavelets (Bior-NSW) family which are proposed by [12], and perform comparative study between the classical Daubechies constructed wavelets, prooved dominance in approximation different kinds signals.