Abstract
Removal of noise is an important step in the image restoration process, and it remains a challenging problem in image processing. Denoising is a process used to remove the noise from the corrupted image, while retaining the edges and other detailed features as much as possible. Recently, denoising in the fractional domain is a hot research topic. The fractional-order anisotropic diffusion method can bring a less blocky effect and preserve edges in image denoising, a method that has received much interest in the literature. Based on this method, we propose a new method for image denoising, in which fractional-varying-order differential, rather than constant-order differential, is used. The theoretical analysis and experimental results show that compared with the state-of-the-art fractional-order anisotropic diffusion method, the proposed fractional-varying-order differential denoising model can preserve structure and texture well, while quickly removing noise, and yields good visual effects and better peak signal-to-noise ratio.
Highlights
Digital images play an important role in many applications, such as astronomy, computer tomography, machine vision, and geographical information systems
Lots of research has been concentrated on this area for a long time, and many methodologies have been proposed by researchers for achieving good performance,[1,2,3,4,5,6] in which partial differential equation (PDE)-based image processing techniques offer great potential in developing image denoising applications with good results
We propose a new image-denoising method
Summary
Digital images play an important role in many applications, such as astronomy, computer tomography, machine vision, and geographical information systems. Lots of research has been concentrated on this area for a long time, and many methodologies have been proposed by researchers for achieving good performance,[1,2,3,4,5,6] in which partial differential equation (PDE)-based image processing techniques offer great potential in developing image denoising applications with good results. Based on the work of Perona and Malik,[7] which replaces the isotropic diffusion by anisotropic diffusion, many methods connecting adaptive smoothing with systems of nonlinear PDE8–13 have been proposed to preserve important structures in images, while removing noise. We propose a new image-denoising method (named fractional-varying-order differential model).
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