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 paper a robust and accurate algorithm based on Haar wavelet collocation method (HWCM) is proposed for solving eighth order boundary value problems. We used the Haar direct method for calculating multiple integrals of Haar functions. To illustrate the efficiency and accuracy of the concerned method, few examples are considered which arise in the mathematical modeling of fluid dynamics an...

I present a method for producing estimates of the intensity function of certain `burst-like' inhomogeneous Poisson processes, based on the shrinkage of Haar wavelet coe cients of the observed counts. The Haar basis is a natural wavelet basis in which to work in this context, and I derive thresholds for shrinkage estimation based on the distribution of the coe cients. The translation-invariant d...

Fingerprint image segmentation is one of the important preprocessing steps in Automatic Fingerprint Identification Systems (AFIS). Segmentation separates image background from image foreground, removing unnecessary information from the image. This paper proposes a new fingerprint segmentation method using Haar wavelet and Kohonen’s Self Organizing Map (SOM). Fingerprint image was decomposed usi...

A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the ...

In their recent paper, Alnasser and Foroosh derive a wavelet-domain (in-band) method for phase-shifting of 2-D "nonseparable" Haar transform coefficients. Their approach is parametrical to the (a priori known) image translation. In this correspondence, we show that the utilized transform is in fact the separable Haar discrete wavelet transform (DWT). As such, wavelet-domain phase shifting can b...

Magnetic resonance imaging (MRI) provides detailed anatomic information of any part of the body. In this method a hybrid approach for classification of brain tissue in MRI based on Particle Swarm Optimization (PSO) and Support Vector Machine (SVM) wavelet based texture feature are extracted from normal and tumor region by using HAAR wavelet. These features are given as input to the SVM classifi...

ABSTRACT: This paper begins by using the Haar wavelet to analyze the cumulative distribution function of a stream of two-valued Bernoulli trials. We find that this function maps binary numbers in [0,1] into non-uniform binary numbers in [0,1]. More generally, for r-valued Bernoulli trials, the distribution function likewise maps usual base-r numbers into non-uniform base-r numbers. We also find...

Abstract: In this paper, identification of a continuous-time linear time-varying (LTV) system is proposed, where Haar wavelet with unit energy is employed. For that purpose, an algebraic equation is derived by expanding the input-output data and the time-varying impulse response using normalized Haar wavelets. Unknown wavelet coefficients for the a LTV system’s impulse response can be effective...

In this paper, an efficient numerical scheme based on uniform Haar wavelets and the quasilinearization process is proposed for the numerical simulation of time dependent nonlinear Burgers’ equation. The equation has great importance in many physical problems such as fluid dynamics, turbulence, sound waves in a viscous medium etc. The Haar wavelet basis permits to enlarge the class of functions ...