We present a general setting where wavelet filters and multiresolution decompositions can be defined, beyond the classical $${\mathbf {L}}^2({\mathbb {R}},dx)$$ setting. This is done in framework of iterated function system (IFS) measures; these include all cases studied so far, particular Julia set/measure cases. Every IFS has fixed order, say N, we show that are indexed by infinite dimensiona...

‎let $g$ be a group with identity $e.$ let $r$ be a $g$-graded‎ ‎commutative ring and $m$ a graded $r$-module‎. ‎in this paper‎, ‎we‎ ‎introduce several results concerning graded classical prime‎ ‎submodules‎. ‎for example‎, ‎we give a characterization of graded‎ ‎classical prime submodules‎. ‎also‎, ‎the relations between graded‎ ‎classical prime and graded prime submodules of $m$ are studied‎.‎

New methods for lossy image compression based on generalized wavelet decompositions have been introduced recently. Unlike in the classical wavelet decomposition scheme it is possible to use diierent scaling and wavelet functions at every scale by using non-stationary multiresolution analyses. This freedom in using diierent functions can be exploited for adaptive compression techniques. In this ...

In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and wavelet denoising to derive a new multiscale interpolation algorithm for piecewise smooth signals. We formulate the optimization of nding the signal that balances agreement with the given samples against a wavelet-domain regularization. For signals in the Besov space B p (Lp), p 1, the optim...

Baseline wander elimination is considered a classical problem. In electrocardiography (ECG) signals, baseline drift can influence the accurate diagnosis of heart disease such as ischemia and arrhythmia. We present a wavelet-transform- (WT-) based search algorithm using the energy of the signal in different scales to isolate baseline wander from the ECG signal. The algorithm computes wavelet pac...

This paper deals with the application of the wavelet transform to hierarchical texture analysis. The main goal is the design of texture-matched FIR-filterbanks as the dyadic (2-channel) orthogonal and the M-channel biorthogonal wavelet filterbanks. The new approach represents a generalization of the already known purely mathematically-oriented design methods for multirate and wavelet filterbank...

The denoising of a natural image corrupted by noise is a classical problem in image processing. In this paper, an efficient algorithm of image denoising based on multi-objective optimization in discrete wavelet transform (DWT) domain is proposed, which can achieve the Pareto optimal wavelet thresholds. First, the multiple objectives for image denoising are presented, then the relation between t...

A wavelet method is proposed for solving a class of nonlinear timedependent partial differential equations. Following this method, the nonlinear equations are first transformed into a system of ordinary differential equations by using the modified wavelet Galerkin method recently developed by the authors. Then, the classical fourth-order explicit Runge-Kutta method is employed to solve the resu...