Abstract
The traditional integer-order partial differential equations and gradient regularization based image denoising techniques often suffer from staircase effect, speckle artifacts, and the loss of image contrast and texture details. To address these issues, in this paper, a difference curvature driven fractional anisotropic diffusion for image noise removal is presented, which uses two new techniques, fractional calculus and difference curvature, to describe the intensity variations in images. The fractional-order derivatives information of an image can deal well with the textures of the image and achieve a good tradeoff between eliminating speckle artifacts and restraining staircase effect. The difference curvature constructed by the second order derivatives along the direction of gradient of an image and perpendicular to the gradient can effectively distinguish between ramps and edges. Fourier transform technique is also proposed to compute the fractional-order derivative. Experimental results demonstrate that the proposed denoising model can avoid speckle artifacts and staircase effect and preserve important features such as curvy edges, straight edges, ramps, corners, and textures. They are obviously superior to those of traditional integral based methods. The experimental results also reveal that our proposed model yields a good visual effect and better values of MSSIM and PSNR.
Highlights
A challenging task in designing image denoising model is to retain significant features, such as edges and texture details, while eliminating noise
Among a variety of integer-order partial differential equations based image denoising techniques [1,2,3], energy minimization based variational technique in two well-known forms of the nonlinear diffusion with anisotropic diffusion proposed by Perona and Malik [4] (Perona-Malik or PM) and total variation (TV) regularization proposed by Rudin et al [5] (Rudin-Osher-Fatemi or ROF) are the ones that have shown a good edge preservation capability
Inspired by fractional-order anisotropic diffusion and the curvature driven diffusion by introducing fractional calculus instead of the curvature, we propose a novel diffusion model for image denoising which uses the difference curvature in the conductance term to describe the intensity variations in images, which is named difference curvature driven fractional-order anisotropic diffusion (DCFAD) and modeled by
Summary
A challenging task in designing image denoising model is to retain significant features, such as edges and texture details, while eliminating noise. Among a variety of integer-order partial differential equations based image denoising techniques [1,2,3], energy minimization based variational technique in two well-known forms of the nonlinear diffusion with anisotropic diffusion proposed by Perona and Malik [4] (Perona-Malik or PM) and total variation (TV) regularization proposed by Rudin et al [5] (Rudin-Osher-Fatemi or ROF) are the ones that have shown a good edge preservation capability. Most of these nonlinear diffusion models are developed from the following model:.
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