In this paper, we develop an accurate and ef£cient Haar wavelet method for well-known FitzHugh-Nagumo equation. The proposed scheme can be used to a wide class of nonlinear reaction-diffusion equations. The power of this manageable method is con£rmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, ¤exible, convenient, small computation costs and computationally attract...

Recently, the information processing approaches are increased. These methods can be used for several purposes: compressing, restoring, and information encoding. The raw data are less presented and are gradually replaced by others formats in terms of space or speed of access. This paper is interested in compression, precisely, the image compression using the Haar wavelets. The latter allows the ...

The theory of periodic wavelet transforms presented here was originally developed to deal with the problem of epileptic seizure prediction. A central theorem in the theory is the characterization of wavelets having time and scale periodic wavelet transforms. In fact, we prove that such wavelets are precisely generalized Haar wavelets plus a logarithmic term. It became apparent that the aforemen...

A new method is presented for computation of optimal control for linear systems using Haar wavelets. The method is based on a novel operational matrix derived from integration of Haar wavelets. The optimal control problem is converted to a two-point-boundary-value problem, which is then solved using the Haar wavelet transformation. The proposed method is then extended to the numerical solution ...

In this work, a composite numerical scheme based on finite difference and Haar wavelets is proposed to solve time dependent coupled Burgers’ equation with appropriate initial and boundary conditions. Time derivative is discretized by forward difference and then quasilinearization technique is used to linearize the coupled Burgers’ equation. Space derivatives discretization with Haar wavelets le...

Abstract – This paper introduces some foundations of wavelets over Galois fields. Standard orthogonal finite-field wavelets (FFWavelets) including FF-Haar and FFDaubechies are derived. Non-orthogonal FFwavelets such as B-spline over GF(p) are also considered. A few examples of multiresolution analysis over Finite fields are presented showing how to perform Laplacian pyramid filtering of finite ...

In order to get an efficient image representation we introduce a new adaptive Haar wavelet transform, calledTetrolet Transform. Tetrolets are Haar-type wavelets whose supports are tetrominoes which are shapes made by connecting four equal-sized squares. The corresponding filter bank algorithm is simple but enormously effective. Numerical results show the strong efficiency of the tetrolet transf...

Investigation of various wavelet methods, for its capability of analyzing various dynamic phenomena through waves gained more and more attention in engineering research. Starting from ‘offering good solution to differential equations’ to capturing the nonlinearity in the data distribution, wavelets are used as appropriate tools that provide good mathematical model for scientific phenomena, whic...

Since the publication, less than ten years ago, of Mallat's paper on Mul-tiresoltion Analysis Ma], and Daubechies' paper on the construction of smooth compactly supported wavelets D], wavelets had gained enormous popularity in mathematics and in the application domains. It is suucient to note that there are currently more than 10,000 subscribers to the monthly Wavelet Digest. At the same time, ...

This paper proposes a robust watermarking technique using wavelets of well-known transforms DCT, Walsh and Haar. HL and LH bands are separately selected for watermark insertion. While inserting watermark, its energy is varied with 40% margin to original energy of region of host selected for insertion of watermark to study effect on robustness. Performance of proposed technique is evaluated agai...