A simple and flexible modification of Grünwald–Letnikov fractional derivative in image processing

This article presents a novel four-dimensional autonomous fractional-order chaotic system (FOCS) with multi-nonlinearity terms. Several dynamics, such as the chaotic attractors, equilibrium points, fractal dimension, Lyapunov exponent, and bifurcation diagrams of this new FOCS, are studied analytically and numerically. Adaptive control laws are derived based on Lyapunov theory to achieve chaos synchronization between two identical new FOCSs with an uncertain parameter. For these two identical FOCSs, one represents the master and the other is the slave. The uncertain parameter in the slave side was estimated corresponding to the equivalent master parameter. Next, this FOCS and its synchronization were realized by a feasible electronic circuit and tested using Multisim software. In addition, a microcontroller (Arduino Due) was used to implement the suggested system and the developed synchronization technique to demonstrate its digital applicability in real-world applications. Furthermore, based on the developed synchronization mechanism, a secure communication scheme was constructed. Finally, the security analysis metric tests were investigated through histograms and spectrograms analysis to confirm the security strength of the employed communication system. Numerical simulations demonstrate the validity and possibility of using this new FOCS in high-level security communication systems. Furthermore, the secure communication system is highly resistant to pirate attacks. A good agreement between simulation and experimental results is obtained, showing that the new FOCS can be used in real-world applications.

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“…With Γ(1) = 1; Γ(0) = +∞. Grunwald-Letnikov approaches the fractional derivative, as demonstrated in the following [52].…”

Section: Fractional Order Preliminariesmentioning

confidence: 94%

A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

et al. 2021

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“…Many dramatic changes in this area have been made by taking the fractional differential concepts into account. In recent years, the use of fractional differential operators to improve image quality, image texture enhancement, image noise reduction, and image edge analysis have yielded stunning results [4][5][6][7][8][9][10][11][12]. One of the most important formulas for expanding of fractional differential operators in image processing is to use the following general form:…”

Section: A Short Review Of Some Of the Well-known Methodsmentioning

confidence: 99%

“…Using the general structures presented in (5) and (6), then utilizing the coefficients of σ s obtained in (17), two new masks can be used to determine the edges of an image outlined in what follows.…”

Section: The Masks Based On the Grunwald-letnikov (Gl) Approximationmentioning

confidence: 99%

Some new edge detecting techniques based on fractional derivatives with non-local and non-singular kernels

2020

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Computers and electronics play an enormous role in today's society, impacting everything from communication and medicine to science. The development of computer-related technologies has led to the emergence of many new important interdisciplinary fields, including the field of image processing. Image processing tries to find new ways to access and extract information from digital images or videos. Due to this great importance, many researchers have tried to utilize new and powerful tools introduced in pure and applied mathematics to develop new concepts in imaging science. One of these valuable research areas is the contents of fractional differential calculus. In recent years, extensive applications to the new fractional operators have been employed in real-world problems. This article attempts to address a practical aspect of this era of research in the edge detecting of an image. For this purpose, two general structures are first proposed for making new fractional masks. Then the components in these two structures are evaluated using the fractional integral Atangana-Baleanu operator. The performance and effectiveness of these proposed designs are illustrated by several numerical simulations. A comparison of the results with the results of several well-known masks in the literature indicates that the results presented in this article are much more accurate and efficient. This is the main achievement of this article. These fractional masks are all novel and have been introduced for the first time in this contribution. Moreover, in terms of computational cost, the proposed fractional masks require almost the same amount of computations as the existing conventional ones. By observing the numerical simulations presented in the paper, it is easily understood that with proper adjustment for the fractional-order parameter, the accuracy of the obtained results can be significantly improved. Each of the new suggested structures in this article can be regarded as a valid and effective alternative for the well-known existing kernels in identifying the edges of an image.

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“…Image denoising inside the fractional area has lately obtained extensive research attention [4,5]. Several algorithms on fractional calculus for image denoising were proposed [6,7]. On the contrary the property of integral differential, the constant fractional differential is non-zero, while their integral differential should be a zero one [8,9].…”

Section: Introductionmentioning

confidence: 99%

An Effective Denoising and Enhancement Strategy for Medical Image Using Rl-Gl-Caputo Method

Ganga

Janakiraman

Sivaraman

et al. 2021

Advances in Parallel Computing

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At present, fractional differential is the effective mathematical approach which deals with the factual problems. This projected technique employs the fractional derivatives definitions Riemann-Liouville (R-L), Grunwald-Letnikov (G-L) and the caputo technique for denoising medical image. The presented method based on fractional derivative which in turn improves the quality of image. The input image is processed on integer order method such as pre-processing operation, image conversion and noise image. The fractional differential mask method is to be applied with the help of Riemann Liouville, and Caputo algorithm. After denoising the medical image enhanced using Anisotropic diffusion process and the result is analyzed to finally get denoised and predicted image.

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A simple and flexible modification of Grünwald–Letnikov fractional derivative in image processing

Cited by 13 publications

References 12 publications

A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

A New Fractional-Order Chaotic System with Its Analysis, Synchronization, and Circuit Realization for Secure Communication Applications

Some new edge detecting techniques based on fractional derivatives with non-local and non-singular kernels

An Effective Denoising and Enhancement Strategy for Medical Image Using Rl-Gl-Caputo Method

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