Wavelets can be thought of as a set of well-localized basis functions with very good approximation properties. The diiculty in applying wavelet approximation to high-dimensional data is that the number of basis functions increases exponentially with the number of dimensions, making the application of standard mathematical methods for determining coeecients diic ult. We propose a modeling method...

In order to get divergence free and curl free wavelets, one introduced the smoothed pseudo spline by using the convolution method. The smoothed pseudo splines can be considered as an extension of pseudo splines. In this paper, we first show that the shifts of a smoothed pseudo spline are linearly independent. The linear independence of the shifts of a pseudo spline is a necessary and sufficient...

In this work, we present a new low memory requirement and low computational time method for solving a class of integral equation of the second kind which is based on the use of B-Spline wavelets. Because of vanishing moments and compact support and semiorthogonality properties of these wavelets, operational matrix of the method is very sparse. Also, applying some appropriate thresholding parame...

We introduce a new class of wavelets that behave like a given differential operator L. Our construction is inspired by the derivative-like behavior of classical wavelets. Within our framework, the wavelet coefficients of a signal y are the samples of a smoothed version of L{y}. For a linear system characterized by an operator equation L{y} = x, the operator-like wavelet transform essentially de...

In this paper, we give an algorithm to construct semi-orthogonal symmetric and anti-symmetric M-band wavelets. As an application, some semi-orthogonal symmetric and anti-symmetric M-band spline wavelets are constructed explicitly. Also we show that if we want to construct symmetric or anti-symmetric M-band wavelets from a multiresolution, then that multiresolution has a symmetric scaling function.

The paper investigates new robust code constructions based on bent functions and spline–wavelet transformation. Implementation of in construction increases the probability error detection data channel cryptographic devices. Meanwhile, use spline wavelet theory for constructing codes gives possibility to increase system security from actions an attacker. Presented combine spline-wavelets functio...

Glossary 5 Introduction 6 Definition of Wavelets 7 Definition of Filters 8 Multi-Resolution Analysis 9 Wavelet Decomposition and Reconstruction 10 Refinable Functions 11 Compactly Supported Orthonormal Wavelets 12 Parameterization of Orthonormal Wavelets 13 Biorthogonal Wavelets 14 Prewavelets 15 Tight Wavelet Frames 16 Tight Wavelet Frames over Bounded Domain 17 q-Dilated Orthonormal Wavelets ...