Correspondence between multiwavelet shrinkage and nonlinear diffusion

Alkhidhr, Hanan A.; Jiang, Qingtang

doi:10.1016/j.cam.2020.113074

Cited by 6 publications

(2 citation statements)

References 47 publications

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“…Researchers now a days are very much interested in the topic of solute transportation and that is why there are lots of methods found in recent years to solve several different models depicting solute transportation. Presently, many problems with different concepts of science are related with the non‐linear equations [1–3]. During literature survey, various models on non‐linear problems have been found [4–8].…”

Section: Introductionmentioning

confidence: 99%

Solution of variable‐order partial integro‐differential equation using Legendre wavelet approximation and operational matrices

et al. 2022

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This article is concerned with developing a method to find a numerical solution of a one-dimensional variable-order non-linear partial integro-differential equation (PIDE) viz., reaction-advection-diffusion equation with initial and boundary conditions. The proposed numerical scheme shifted Legendre collocation method is based on operational matrices. The operational matrices using one-dimensional wavelets are derived to solve the said variable-order model.First operational matrices have been introduced for integration and variableorder derivatives using one-dimensional Legendre wavelets (LWs). After that, using the shifted Legendre collocation points, the model is reduced to a system of algebraic equations, which are solved using Newton-Cotes method. The error is then calculated by comparing the numerical solution obtained from the system of algebraic equations and the known exact solution of an existing problem to validate the efficiency of the proposed numerical scheme. The main contribution of the article is the graphical exhibitions of the solution profile for different variable order derivatives in presence of different values of the parameters.

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Section: Introductionmentioning

confidence: 99%

Solution of variable‐order partial integro‐differential equation using Legendre wavelet approximation and operational matrices

et al. 2022

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“…This added flexibility is for example advantageous in multiwavelet denoising, which has been applied in rolling bearing fault detection [13][14][15][16], and in the load spectrum of computer numerical control lathe [17]. Recently, the correspondence between multiwavelet shrinkage and nonlinear diffusion was studied [18]. We will be addressing orthogonal multiwavelets with compact support generated from filter banks with a complexity (filter order) that can be chosen by the user.…”

Section: Introductionmentioning

confidence: 99%

The Design of Matched Balanced Orthogonal Multiwavelets

Karel

Steenkiste

Peeters

2022

Front. Appl. Math. Stat.

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The theory of orthogonal multiwavelets offers enhanced flexibility for signal processing applications and analysis by employing multiple waveforms simultaneously, rather than a single one. When implementing them with polyphase filter banks, it has been recognized that balanced vanishing moments are needed to prevent undesirable artifacts to occur, which otherwise compromise the interpretation and usefulness of the multiwavelet analysis. In the literature, several such balanced orthogonal multiwavelets have been constructed and published; but however useful, their choice is still limited. In this work we present a full parameterization of the space of all orthogonal multiwavelets with two balanced vanishing moments (of orders 0 and 1), for arbitrary given multiplicity and degree of the polyphase filter. This allows one to search for matching multiwavelets for a given application, by optimizing a suitable design criterion. We present such a criterion, which is sparsity-based and useful for detection purposes, which we illustrate with an example from electrocardiographic signal analysis. We also present explicit conditions to build in a third balanced vanishing moment (of order 2), which can be used as a constraint together with the earlier parameterization. This is demonstrated by constructing a balanced orthogonal multiwavelet of multiplicity three, having three balanced vanishing moments, but this approach can easily be employed for arbitrary multiplicity.

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Cluster Adaptive Stationary Wavelet Diffusion

Mandava

Regentova

2022

Advances in Intelligent Systems and Computing

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Correspondence between multiwavelet shrinkage and nonlinear diffusion

Cited by 6 publications

References 47 publications

Solution of variable‐order partial integro‐differential equation using Legendre wavelet approximation and operational matrices

Solution of variable‐order partial integro‐differential equation using Legendre wavelet approximation and operational matrices

The Design of Matched Balanced Orthogonal Multiwavelets

Cluster Adaptive Stationary Wavelet Diffusion

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