We consider a class of discrete differential operators acting on multidimensional Haar wavelet basis with the aim of finding wavelet approximate solutions of partial differential problems. Although these operators depend on the interpolating method used for the Haar wavelets regularization and the scale dimension space, they can be easily used to define the space of approximate wavelet solution...

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...

ORTHOGONAL AND SYMMETRIC HAAR WAVELETS ON THE THREE-DIMENSIONAL BALL Andy Chow Master of Science Graduate Department of Computer Science University of Toronto 2010 Spherical signals can be found in a wide range of fields, including astronomy, computer graphics, medical imaging and geoscience. An efficient and accurate representation of spherical signals is therefore essential for many applicati...

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 ...

Objective of our paper is to present the Haar wavelet based solutions of boundary value problems by Haar collocation method and utilizing Quasilinearization technique to resolve quadratic nonlinearity in y. More accurate solutions are obtained by wavelet decomposition in the form of a multiresolution analysis of the function which represents solution of boundary value problems. Through this ana...

Estimating the gravity anomaly causative bodies boundary can facilitate the gravity field interpretation. In this paper, 2D discrete wavelet transform (DWT) is employed as a method to delineate the boundary of the gravity anomaly sources. Hence, the GRACE’ satellite gravity data is decomposed using DWT. DWT decomposites a single approximation coefficients into four distinct components: the appr...

In this paper, we present a numerical scheme using uniform Haar wavelet approximation and quasilinearization process for solving some nonlinear oscillator equations. In our proposed work, quasilinearization technique is first applied through Haar wavelets to convert a nonlinear differential equation into a set of linear algebraic equations. Finally, to demonstrate the validity of the proposed m...