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Hybrid Equation Resulting from the Combination of a Second-Order Equation with a Fourth-Order Equation for the Restoration of Noisy Images

Simo Thierry*, Ntsama Eloundou Pascal**, Noura Alexendre***

* - *** Department of Physics, University of Ngaoundere, Ngaoundere, Cameroon.

Periodicity:January - March'2020
DOI : https://doi.org/10.26634/jip.7.1.17038

Abstract

The filtering of images is an important task in the research area of image processing. The diffusion equations are frequently used in image processing to solve the problem of staircase effect introduced by the second order diffusion equations. Different equations dissemination of fourth order is proposed to improve the filtering performance. However, the diffusion equations of order four suffer from the problems of on-smoothing of the staircase effect and a very slow convergence towards the solution. In this paper, a hybrid equation that uses a convex combination to associate the second-order equation of Wang in the equation of the fourth-order Lysaker is proposed to reap the benefits of two equations combined for restoring noisy images. In this hybrid equation, a diffusion coefficient which uses the Z-shaped fuzzy logic membership function is proposed to limit the diffusion of strong gradients produced by the equation of the second order Wang et al for better preserve the contours of the image. The experimental results illustrate the effectiveness of the proposed model in image restoration.

Keywords

Partial Differential Equation (PDE), Gradient Vector Convolution (GVC), Restoration, Diffusion Coefficient, Noise.

How to Cite this Article?

Thierry, S., Pascal, N. E., and Alexendre, N. (2020). Hybrid Equation Resulting from the Combination of a Second-Order Equation with a Fourth-Order Equation for the Restoration Noisy Images. i-manager's Journal on Image Processing , 7(1), 24-34. https://doi.org/10.26634/jip.7.1.17038

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