Abstract: In this article a numerical method is proposed to approximate the solution of the system of integrodifferential equations describing biological species living together. The method is based upon Legendre multiwavelet approximations. The properties of Legendre multiwavelet are first presented. These properties together with Ritz-Galerkin method are then utilized to reduce the equations ...

A Legendre multiwavelet based method is developed in this paper to solve second kind hypersingular integral equation by converting it into a Cauchy singular integro-differential equation. Multiscale representation of the singular and differential operators is obtained by employing Legendre multiwavelet basis. An estimate of the error of the approximate solution of the integral equation is obtai...

In recent years, wavelet-based video compressions have become a major focus of research because of the advantages that it provides. More recently, a growing thrust of studies explored the use of multiple scaling functions and multiple wavelets with desirable properties in various fields, from image de-noising to compression. In term of data compression, multiple scaling functions and wavelets o...

Translation invariant (TI) single wavelet de-noising was developed by Coifman and Donoho and they show that TI is better than non-TI single wavelet de-noising. On the other hand, Strela et al. have found that non-TI multiwavelet de-noising gives better results than non-TI single wavelets. In this paper we extend Coifman and Donoho's TI single wavelet de-noising scheme to multiwavelets. Experime...

It is very important for generating an orthonormal multiwavelet system to construct a conjugate quadrature filter (CQF). In this paper, a general method of constructing a length-J + 1 CQF with multiplicity r and scale a from a length-J CQF is obtained. As a special case, we study generally the construction of a length-J + 1 CQF with multiplicity 2 and scale 2 which can generate a compactly supp...

With the development of micro electronics and information technology, there are more pixels in unit area of the imaging device. The high resolution images with more pixels can be obtained easily. But the high resolution images have huge data volume. It is difficult to transmit, to process, to store high resolution images. So compressing images is an important technology to reduce the requisite ...

In the paper, two pre-processing methods for load forecast sampling data including multiwavelet transformation and chaotic time series are introduced. In addition, multi neural network for load forecast including BP artificial neural network, RBF neural network and wavelet neural network are introduced, too. Then, a combination load forecasting model for power load based on chaotic time series,...

The joint spectral radius ρ of 2 matrices is related to the boundedness of all their products. Calculating ρ is known to be NP-hard. In this work we estimate the joint spectral radius associated to a bidimensional separable multiwavelet, in order to analyze its Hölder continuity. To the author’s knowledge this has not been done. The analysis aims at testing the aplicability of the multiwavelet ...

An efficient projection procedure is derived for use of orthogonal multiwavelets in the analysis of discrete data sequences. A family of simple prefilters corresponding to numerical quadrature evaluation of the projection integrals provides exact results for locally-polynomial data. The full approximation order of the multiwavelet basis can thus always be enabled. For nonpolynomial signals, the...

This paper presents the evaluation of robustness for image watermarking techniques in the multiwavelet transform domain. The first one is based on the concept of the watermarking technique that has been designed in the previous chapter and the second one is based on the code division multiple access (CDMA) technique. The embedding information is a visually recognizable pattern which can be extr...