The discrete wavelet transform (DWT) is usually carried out by filterbank iteration; however, for a fixed number of zero moments, this does not yield a discrete-time basis that is optimal with respect to time localization. This paper discusses the implementation and properties of an orthogonal DWT, with two zero moments and with improved time localization. The basis is not based on filterbank i...

In this paper we solve the Laplace equation by solving a boundary integral equation in a wavelet basis. In wavelet basis the discretized equations preserve their good conditioning while their sparse structures speed up iterative solvers. We analyze the behavior of GCR algorithms under wavelet transformations and in non-standard form, the optimal choice of Daubechies lters and truncation strateg...

This paper is the second part of a work on stabilizing the classical hierarchical basis HB by using wavelet-like basis functions. Implementation techniques are of major concern for the multilevel preconditioners proposed by the authors in the first part of the work, which deals with algorithms and their mathematical theory. Numerical results are presented to confirm the theory established there...

In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented...

The quaternion wavelet transform is a new multiscale analysis tool. Firstly, this paper studies the standard orthogonal basis of scale space and wavelet space of quaternion wavelet transform in spatial L2 R2 , proves and presents quaternion wavelet’s scale basis function and wavelet basis function concepts in spatial scale space L2 R2;H , and studies quaternion wavelet transform structure. Fina...

Recently discrete wavelet transform and wavelet packet has emerged as popular techniques for image compression. The wavelet transform is one of the major processing components of image compression. The results of the compression change as per the basis and tap of the wavelet used. This paper compares compression performance of Daubechies, Biorthogonal, Coiflets and other wavelets along with res...

We present a forecasting strategy based on stationary wavelet transform combined with radial basis function (RBF) neural network to improve the accuracy of 3-month-ahead hake catches forecasting of the fisheries industry in the central southern Chile. The general idea of the proposed forecasting model is to decompose the raw data set into an annual cycle component and an inter-annual component ...

This paper describes a novel application of support vector machines and multiscale texture and color invariants to a problem in biological oceanography: the identification of 6 species of bivalve larvae. Our data consists of polarized color images of scallop and other bivalve larvae (between 2 and 17 days old) collected from the ocean by a shipboard optical imaging system of our design. Larvae ...

This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel‎. ‎First‎, ‎a collocation method based on Haar wavelets (HW)‎, ‎Legendre wavelet (LW)‎, ‎Chebyshev wavelets (CHW)‎, ‎second kind Chebyshev wavelets (SKCHW)‎, ‎Cos and Sin wavelets (CASW) and BPFs are presented f...