Fractional-order diffusion coupled with integer-order diffusion for multiplicative noise removal

Li, Chengxue; He, Chu

doi:10.1016/j.camwa.2023.01.036

Cited by 15 publications

(5 citation statements)

References 74 publications

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“…Since fractional differential operators involve integrals defined over a time domain, which will lead to significant genetic and memory effects [13]. As a result, fractional calculus has received great attention in the last few decades and has been extensively studied in many fields such as nonlinear oscillators, control systems, diffusion problems, viscoelastic mechanics, rheology and so on [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Taming chaos in generalized Liénard systems by the fractional-order feedback based on Melnikov analysis

Huang

2023

Phys. Scr.

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The dynamical behavior of Liénard systems has always been a hot topic in nonlinear analysis. In the present study, a simple fractional-order feedback controller is put forward to tame chaos for a class of forced generalized Liénard systems. Adopting harmonic balance method, the first-order approximate equivalent integer-order system of the original fractional-order system is deduced. Then the criterion for taming chaos is established by employing the Melnikov approach. Duffing-Rayleigh chaotic oscillator is taken as an example to illustrate the validity of the proposed method. Firstly, the critical feedback intensity and differential order for taming chaos are obtained by the proposed criterion. Then, multiple numerical indicators such as phase portrait, time history plot, Lyapunov exponent and bifurcation diagram are provided to assist in analyzing theoretical results.

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Section: Introductionmentioning

confidence: 99%

Taming chaos in generalized Liénard systems by the fractional-order feedback based on Melnikov analysis

Huang

2023

Phys. Scr.

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“…Since the image texture structure is usually non-local in nature, the image texture structure obtained by existing first-or second-order denoising models is usually easily blurred. Unlike the integer-order operator, the fractional-order differential operator is a nonlocal operator [22,23] which can achieve texture detection by inductively obtaining the autocorrelation of an image with different weight coefficients based on the proximity relationship between individual pixel points of the image. Therefore, the second type introduces the nonlinear diffusion equations of their fractional-order derivative, which can be seen as the generalization of the integer-order derivative.…”

Section: Introductionmentioning

confidence: 99%

Multiplicative Noise Removal and Contrast Enhancement for SAR Images Based on a Total Fractional-Order Variation Model

Zhou

Guo

et al. 2023

Fractal Fract

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In this paper, we propose a total fractional-order variation model for multiplicative noise removal and contrast enhancement of real SAR images. Inspired by the high dynamic intensity range of SAR images, the full content of the SAR images is preserved by normalizing the original data in this model. Then, we propose a degradation model based on the nonlinear transformation to adjust the intensity of image pixel values. With MAP estimator, a corresponding fidelity term is introduced into the model, which is beneficial for contrast enhancement and bias correction in the denoising process. For the regularization term, a gray level indicator is used as a weighted matrix to make the model adaptive. We first apply the scalar auxiliary variable algorithm to solve the proposed model and prove the convergence of the algorithm. By virtue of the discrete Fourier transform (DFT), the model is solved by an iterative scheme in the frequency domain. Experimental results show that the proposed model can enhance the contrast of natural and SAR images while removing multiplicative noise.

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“…Fractional calculus is characterized by long-term memory, non-locality, and weak singularity [29].In recent years, fractional-order methods have achieved important applications in the field of engineering, attracting more and more scholars. Research interests in the field of fractional calculus include various topics such as fractional-order image processing [30][31][32], fractional-order control theory [33,34], and fractional-order digital signal processing [35,36]. In the image processing domain, using integer-order operators can enhance the high-frequency portion of the image but also cause information loss in the low-frequency portion.…”

Section: Introductionmentioning

confidence: 99%

Image Edge Detection Based on Fractional-Order Ant Colony Algorithm

Liu

2023

Fractal Fract

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Edge detection is a highly researched topic in the field of image processing, with numerous methods proposed by previous scholars. Among these, ant colony algorithms have emerged as a promising approach for detecting image edges. These algorithms have demonstrated high efficacy in accurately identifying edges within images. For this paper, due to the long-term memory, nonlocality, and weak singularity of fractional calculus, fractional-order ant colony algorithm combined with fractional differential mask and coefficient of variation (FACAFCV) for image edge detection is proposed. If we set the order of the fractional-order ant colony algorithm and fractional differential mask to ν = 0 , the edge detection method we propose becomes an integer-order edge detection method. We conduct experiments on images that are corrupted by multiplicative noise, as well as on an edge detection dataset. Our experimental results demonstrate that our method is able to detect image edges, while also mitigating the impact of multiplicative noise. These results indicate that our method has the potential to be a valuable tool for edge detection in practical applications.

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Fractional-order diffusion coupled with integer-order diffusion for multiplicative noise removal

Cited by 15 publications

References 74 publications

Taming chaos in generalized Liénard systems by the fractional-order feedback based on Melnikov analysis

Taming chaos in generalized Liénard systems by the fractional-order feedback based on Melnikov analysis

Multiplicative Noise Removal and Contrast Enhancement for SAR Images Based on a Total Fractional-Order Variation Model

Image Edge Detection Based on Fractional-Order Ant Colony Algorithm

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