Abstract
A nonlinear anisotropic hybrid diffusion equation is discussed for image denoising, which is a combination of mean curvature smoothing and Gaussian heat diffusion. First, we propose a new edge detection indicator, that is, the diffusivity function. Based on this diffusivity function, the new diffusion is nonlinear anisotropic and forward-backward. Unlike the Perona-Malik (PM) diffusion, the new forward-backward diffusion is adjustable and under control. Then, the existence, uniqueness, and long-time behavior of the new regularization equation of the model are established. Finally, using the explicit difference scheme (PM scheme) and implicit difference scheme (AOS scheme), we do numerical experiments for different images, respectively. Experimental results illustrate the effectiveness of the new model with respect to other known models.
Highlights
Image restoration and smoothing are important in problems ranging from medical diagnostic tests to defense applications such as target recognition
From the models mentioned above, we can see that based on the partial differential equations (PDEs) framework, the diffusivity functions affect the quality of the reconstructed image
Noise removal is a difficult problem that arises in various applications relevant to active imaging system
Summary
Image restoration and smoothing are important in problems ranging from medical diagnostic tests to defense applications such as target recognition. The blocky solution fails to satisfy visual impression and can develop false edges, which can mislead a human or computer into identifying erroneous features, not present in the true image Some authors consider another regularizing term to remove the noise [34], which is as follows: inuf. From the models mentioned above, we can see that based on the PDE framework, the diffusivity functions affect the quality of the reconstructed image. In this paper, based on a new diffusivity function, we propose a new image denoising model which generalizes the approaches due to Perona and Malik [2], Chen et al [35], and El-Fallah and Ford [42]. We will give the numerical results which indicate the new model is able to preserve edges and denoise better than the existing methods, for instance, the TV model and PM model
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