Image Denoising Based on Adaptive Fractional Order with Improved PM Model

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.

Image denoising method based on variable exponential fractional‐integer‐order total variation and tight frame sparse regularization

“…Firstly, we did experiments with the five test images with different noise levels. Then, we compared our proposed method with VarPTV model [2], VarPFTV model (our model with and ) and IPM model [23]. Secondly, in order to further validate the effectiveness and increase the possibility of application of our proposed method, we also did experiments with two real images of low‐dose (10 mAs) head phantom CBCT reconstructed data provided by the laboratory of Shandong Xinhua Medical Instrument Co., Ltd., and gave comparison results.…”

An efficient feature-preserving PDE algorithm for image denoising based on a spatial-fractional anisotropic diffusion equation

“…In recent years, fractional order PDE based methods have attracted more and more research interest due to their ability to balance the noise removal and the preservation of image edges and textures; see, e.g. [1,10,11,19,20,36,38]. Numerical experiments reveal that these methods are able to alleviate both the staircase and speckle effects and generate processed images of higher quality than the integer order PDE based methods.…”

Perona-Malik Model with Diffusion Coefficient Depending on Fractional Gradient via Caputo-Fabrizio Derivative

“…The maximum flow is generated at locations where |∇u | = K [7]. The Perona-Malik equation (6) and the large amount of its modifications [5,[8][9][10][11] have demonstrated to be able to achieve a good trade-off between noise removal and edge preservation. Unfortunately, edge-stopping functions lead to backward-forward problems that are ill-posed [1]; for this reason, in [8,12], authors introduced a modification in the diffusion coefficient to obtain a regularized version as follows:…”

“…In [22], it is said that the basic reason for locating edge positions falsely is that the fractional-order gradient module cannot be used as an edge indicator; therefore, the authors in [22] adopted a so-called external fractional-order gradient vector Perona-Malik diffusion by only replacing integer-order derivatives of the external gradient vector to their fractional-order counterparts while keeping first-order derivatives for diffusion coefficient. The model is the same as [9] except for the derivative used in the diffusion coefficient. A novel fractional PDE model is given by Guidotti and Longo in [23]; they address the wellposedness of the following fourth-order model for noise removal, using fractional derivatives defined by Fourier transform.…”

“…where g is given by (9) and s = ∇uðx, y, tÞ and v = ∇ α uðx, y, tÞ . This means that the graph of function (28) is a surface.…”