Noise-enhanced nonlinear PDE for edge restoration in scalar images

Abstract

The report proposed an interpretation for the mechanism of noise-enhanced image restoration with nonlinear PDE (Partial Differential Equation) recently demonstrated in literature. A link is established between the action of noise in a nonlinear Perona-Malik anisotropic diffusion and stochastic resonance in memoryless nonlinear systems for 1-D signals.Index Terms-stochastic resonance, anisotropic diffusion, image restoration, nonlinear image processing.

Non-Linear Low-Level Image Processing Improvement by a Purposely Injection of Noise

“…The goal of this article is to propose a direct application of SR phenomenon in image processing, for the interest of SR in that domain is growing-up. As authors have already shown it in (Histace and Rousseau, 2006;Histace and Rousseau, 2010), a possible application field is nonlinear image restoration. Nevertheless, in order to have a better understanding of the process and the constructive action of noise, we propose to study a more simple image processing tool: Image binarisation.…”

On some applications of vibrational resonance on noisy image perception: the role of the perturbation parameters

“…In the context of image denoising and edge preserving, we can cite the famous Perona & Malik process, based on the so-called diffusion equation which rules the heat transfer in its anisotropic form [42,43]. Histace & Rousseau have shown that including an optimal noise intensity inside the function which provides anisotropy allows one to restore images with better visual interest than those obtained with the classical Perona–Malik method [13,44]. Therefore, it is not surprising that noise enhanced image processing goes on to be widely investigated.…”

“…Moreover, it has been shown that SR also plays a crucial role in human visual perception [6]. Thus, different applications have been addressed ranging from signal detection and quantization [7–10] to image processing [11–13]. On the other hand, by mixing, through a nonlinear system, noise and a bi-chromatic excitation consisting of two frequencies, it has been also shown that a ghost frequency, lower than the weakest excitation frequencies, appears in the system response.…”

Locally Oriented Anisotropic Image Diffusion: Application to Phenotyping of Seedlings

“…We apply this strategy to a real world problem from plant science in the next section. For illustration in this work we have taken as in [6] the nonlinear function g(.) in Eq.…”