Abstract
In order to improve the image quality, in this paper, we propose an improved PM model. In the proposed model, we introduce two novel diffusion coefficients and a residual error term and replace the integer differential operator with the fractional differential operator in the PM model. The diffusion coefficients can be used effectively for edge detection and noise removal. The residual error term can help to prevent image distortion. Fractional order differential operator has a good characteristic that it can enhance image texture information while removing image noise. Additionally, in the two new diffusion coefficients, a novel method is proposed for automatically setting parameter k, and it does not need to do any experiments to get the value of k. For the computing fractional order diffusion coefficient, we employ the discrete Fourier transform, and an iterative scheme is carried out in the frequency domain. In the proposed model, not only is the integer differential operator replaced with the fractional differential operator, but also the order of the fractional differentiation is determined adaptively with the local variance. Comparing with some existing models, the experimental results show that the proposed algorithm can not only better suppress noise, but also better preserve edge and texture information. Moreover, the running time is greatly reduced.
Highlights
Image denoising is a critical task in image processing, and the denoising algorithm is widely researched in recent years
In the classical PM model, the gradient value is used in the direction of east, west, south, and north to distinguish variations which are caused by noise or edge in a corrupted image [2]
To solve the shortcomings that the classical PM model is tending to cause staircase effect and lose texture information, we propose an image denoising algorithm based on adaptive fractional order of PM model:
Summary
Image denoising is a critical task in image processing, and the denoising algorithm is widely researched in recent years. Wang et al [14] proposed new second- and fourth-order anisotropic equations for denoising All of these methods mentioned above are gradient dependent where the gradient controls the diffusion process and degrades texture and fine details. Yuan and Liu [21] proposed an anisotropic diffusion model based on a new diffusion coefficient and fractional order differential for image denoising. Bai and Feng [20] proposed a fractional order anisotropic diffusion model for image denoising, and the model can excellently remove noise and save the edge information. The above-mentioned image processing algorithms based on fractional order partial differential equation have made improvement on keeping detailed image information, texture information, good visual effects, and image denoising.
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