NUMERICAL SOLUTIONS OF THE NONLINEAR POROUS MEDIA EQUATION BASED ON HIGH EXPLORATION PARTICLE SWARM OPTIMIZATION AND MOVING LEAST SQUARES

In this study, a new numerical method based on the combination of High Exploration Particle Swarm Optimization (HEPSO) and Moving Least Squares (MLS) is introduced to solve nonlinear porous media equations. The MLS scheme is employed to describe an appropriate discretized function, and the penalty method is implemented to convert the constrained problem into an unconstrained one via satisfying the initial conditions. The identified objective function is minimized by the HEPSO to find the approximated nodal values for the nonlinear porous media equation. In order to illustrate the effectiveness of the HEPSO, the optimization trajectories are compared with those of a Standard Particle Swarm Optimization (SPSO) algorithm. Moreover, comparisons are made between the exact solution and the introduced strategy to expose the accuracy, effectiveness and simplicity of the proposed method.

Anomalous Diffusion Paradigm for Image Denoising Process

Anisotropic and isotropic diffusion equations have been extensively applied on biomedical image processing for many years and a great diversity of algorithm have been proposed by the scientific community. Here, it is available a recent new implementation of the anomalous diffusion equation, based on the Fokker-Planck PDE diffusion equation (also known as the Porous Media equation). The major contribution of the anomalous process in the image processing area is the possibility to regulates a sub or super-diffusion characteristic in the noise attenuation problem, which have been showed as a suitable solution for the preservation of fine details in complex objects such as the human brain. An ITK Module is offered here in order to easily add the Anisotropic Anomalous Diffusion (AAD) and Isotropic Anomalous Diffusion (IAD) filters in the ITK hierarchy.