Discrete wavelet transform (DWT) is an efficient tool for multi-resolution decomposition of images. It has been shown to be very promising due to its high compression ratio and self-similar data structure. Conventionally a 2-D DWT is accomplished by performing two 1-D operations: one along the rows and the other along the columns of an image. Without executing ordered 1-D transforms, we develop...

In this paper we study the algebraic and geometric structure of the space of compactly supported biorthogonal wavelets. We prove that any biorthogonal wavelet matrix pair (which consists of the scaling lters and wavelet lters) can be factored as the product of primitive parau-nitary matrices, a pseudo identity matrix pair, an invertible matrix, and the canonical Haar matrix. Compared with the f...

this paper presents a proof of stirling's formula using haar wavelets and some properties of hilbert space, such as parseval's identity. the present paper shows a connection between haar wavelets and certain sequences.

We consider a diusion process (Xt) t≥0 , with drift b(x) and diusion coecient σ(x). At discrete times t k = kδ for k from 1 to M , we observe noisy data of the sample path, Y kδ = X kδ + ε k. The random variables (ε k) are i.i.d, centred and independent of (Xt). The process (Xt) t≥0 is assumed to be strictly stationary, β-mixing and ergodic. In order to reduce the noise eect, we split data into...

In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a ...

The Euclidean group (Rn,+) where (n?N, plays a key role in harmonic analysis. If we consider the Lebesgue measure ()nd?xR as the Haar measure of this group then 12(2)()nd?x=d?RR. In this article we look for LCA groups K, whose Haar measures have a similar property. In fact we will show that for some LCA groups K with the Haar measure K?, there exists a constant such that 0KC>()(2)KKK?A=C?A for ...

A conjecture has previously been made on the chaotic behavior of the eigenvectors of a class of n-dimensional random matrices, where n is very large [ Evidence supporting the conjecture has been given in the form of two limit theorems, as n-. relating the random matrices to matrices formed from the Haar measure, h,, on the orthogonal group The present paper considers a reformulation of the conj...

this paper presents a proof of stirling's formula using haar wavelets and some properties of hilbert space, such as parseval's identity. the present paper shows a connection between haar wavelets and certain sequences.