Novel Linear Image Denoising Approach Based on a Modified Gaussian Filter Kernel

Abstract

A Gaussian noise reduction technique for grayscale images is proposed in this article. It uses a modified Gaussian filter kernel based on a hyperbolic second-order equation. The introduced mathematical model differs from the classic Gaussian model provided by the heat equations, by a localization property. Our filtering approach reduces the amount of Gaussian noise and alsoenhances the image contrast. Some image denoising experiments that prove the effectiveness of the proposed method are also described in this article.

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“…The linear isotropic diffusion (heat) equation is the oldest and best investigated PDE method in image processing. To determine the linear isotropic diffusion equation first begins with the general diffusion equation, which is defined as [180]:…”

“…Nevertheless, it smoothes noise within a region in the same way as it blurs semantically important structures like edges, lines, or other details [152]. Additionally, according to Barbu [180], the main disadvantage of this classical procedure is that the denoising operator has no localization property, that is, the solution to the heat equation (Equation 4.16) propagates with infinite speed. In other words, if u 0 = 0 outside a certain domain Ω t , it does not follow that the same thing happens for u (t) outside Ω t ⊂ R N .…”