Publication Date: 2014
Journal Of Medical Signals And Sensors (22287477)4(1)pp. 72-83
Improving the quality of medical images at pre- and post-surgery operations are necessary for beginning and speeding up the recovery process. Partial differential equations-based models have become a powerful and well-known tool in different areas of image processing such as denoising, multiscale image analysis, edge detection and other fields of image processing and computer vision. In this paper, an algorithm for medical image denoising using anisotropic diffusion filter with a convenient stopping criterion is presented. In this regard, the current paper introduces two strategies: utilizing the efficient explicit method due to its advantages with presenting impressive software technique to effectively solve the anisotropic diffusion filter which is mathematically unstable, proposing an automatic stopping criterion, that takes into consideration just input image, as opposed to other stopping criteria, besides the quality of denoised image, easiness and time. Various medical images are examined to confirm the claim.
Publication Date: 2011
Australian Journal of Basic and Applied Sciences (19918178)5(12)pp. 2356-2361
The Adomian decomposition method (ADM) is a numerical method for solving a wide variety of functional equations and usually gets the solution in a series form. In this paper, the technique of Adomian method is used to solve a system of linear integro - differential equations with initial conditions.
Fakharian a., ,
Hamidi beheshti m.t., ,
Davari, A. Publication Date: 2010
International Journal of Computer Mathematics (10290265)87(12)pp. 2769-2785
The aim of this research is to solve the Hamilton-Jacobi-Bellman equation (HJB) arising in nonlinear optimal problem using Adomian decomposition method. First Riccati equation with matrix variable coefficients, arising in linear optimal and robust control approach, is considered. By using the Adomian method, we consider an analytical approximation of the solution of nonlinear differential Riccati equation. An application in optimal control is presented. The solution in different order of approximations and different methods of approximation will be compared with respect to accuracy. Then the HJB equation, obtained in nonlinear optimal approach, is considered and an analytical approximation of the solution of it, using Adomian method, is presented. © 2010 Taylor & Francis.
Publication Date: 2007
International Journal of Computer Mathematics (10290265)84(1)pp. 75-79
In this paper we propose new ideas for the implementation of the Adomian decomposition method to solve nonlinear Volterra integral equations. Numerical examples are presented to illustrate the method for nonlinear Volterra integral equations of the second kind.
Publication Date: 2007
Applied Mathematics and Computation (963003)189(1)pp. 341-345
In this paper, an application of homotopy perturbation method is applied to solve the nonlinear two-dimensional wave equation. The analytic solution of the nonlinear wave equation is calculated in the form of a series with easily computable components. The non-homogenous equation is effectively solved by employing the phenomena of the self-canceling "noise" terms, where sum of components vanishes in the limit. Comparing the methodology with some known techniques shows that the present approach is powerful and reliable. Its remarkable accuracy properties are finally demonstrated by an example. © 2006 Elsevier Inc. All rights reserved.
Publication Date: 2005
Applied Mathematics and Computation (18735649)165(1)pp. 223-227
In this paper, we propose new ideas to implement Adomian decomposition method to solve Volterra integral equations. Numerical examples are presented to illustrate the method for linear Volterra integral equations of the second kind. © 2004 Elsevier Inc. All rights reserved.
Publication Date: 2004
Applied Mathematics and Computation (18735649)153(1)pp. 301-305
In this paper, we propose new ideas to implement Adomian decomposition method to solve integral equations. In this paper we verify use of numerical integration in Adomian's method for cases that evaluation of terms of the series u=∑ui analytically is impossible. © Published by Elsevier Inc.
