Generalized framework for the design of adaptive fractional-order masks for image denoising

Gupta, Anmol; Kumar, Sanjay

doi:10.1016/j.dsp.2021.103305

Cited by 15 publications

(3 citation statements)

References 38 publications

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“…For example, Gupta et al devised an adaptive image-denoising algorithm based on generalised fractional integration and fractional differentiation [9]. They combined this algorithm with an innovative noise-detection method to detect salt-and-pepper noise in images.…”

Section: Introductionmentioning

confidence: 99%

Depth Image Enhancement Algorithm Based on Fractional Differentiation

et al. 2023

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Depth image enhancement techniques can help to improve image quality and facilitate computer vision tasks. Traditional image−enhancement methods, which are typically based on integer−order calculus, cannot exploit the textural information of an image, and their enhancement effect is limited. To solve this problem, fractional differentiation has been introduced as an innovative image−processing tool. It enables the flexible use of local and non−local information by taking into account the continuous changes between orders, thereby improving the enhancement effect. In this study, a fractional differential is applied in depth image enhancement and used to establish a novel algorithm, named the fractional differential–inverse−distance−weighted depth image enhancement method. Experiments are performed to verify the effectiveness and universality of the algorithm, revealing that it can effectively solve edge and hole interference and significantly enhance textural details. The effects of the order of fractional differentiation and number of iterations on the enhancement performance are examined, and the optimal parameters are obtained. The process data of depth image enhancement associated with the optimal number of iterations and fractional order are expected to facilitate depth image enhancement in actual scenarios.

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Section: Introductionmentioning

confidence: 99%

Depth Image Enhancement Algorithm Based on Fractional Differentiation

et al. 2023

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“…Applied Sciences, Control Theory, Economics, Signal and image processing, fractal analysis, thermodynamics, image denoising etc. [1][2][3][4][5][6][7][8][9] Since, the mathematical models based on a fractional order are much more realistic than integer order models due to the fractional derivatives which are more effective to express the memory and heredity properties of different materials and processes. Fractional derivative removes noise effectively while preserves other important information of images like texture and edge details, that is why it has been widely using in image denoising processes.…”

Section: Introductionmentioning

confidence: 99%

Optimization of parameters for image denoising algorithm pertaining to Generalized Caputo-Febrizio Fractional Operator

Gaur

Khan

2023

Preprint

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The aim of the present paper is to optimize the values of different parameters related to the image denoising algorithm involving Caputo Febrizio fractional integral operator of non-singular type with the Mittag-Leffler function in generalized form. The algorithm aims to find the coefficients of a kernel to remove out the noise from images. The optimization of kernel coefficients are done on the basis of the different numerical parameters like Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), Structure Similarity Index measure (SSIM) and Image Enhancement Factor (IEF). The performance of the proposed algorithm is investigated through above mentioned numeric parameters and visual perception with the other prevailed algorithms Experimental results demonstrate that the proposed optimized kernel based on generalized fractional operator performs favorably compared to state of the art methods. The uniqueness of the paper is to highlight the optimized values of performance parameters for different values of fractional orders. Mathematics subject classification: 345A08, 68U10, 94A08.

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“…The Atangana-Baleanu(AB) fractional order derivatives defined by Atangana and Baleanu are widely used in many fields such as biology, control science and engineering, and dynamical system, etc. For example, Owolabi and Atangana [15] used AB fractional order derivatives to build Adams-Bashforth format to model chaotic problems; Abdullahi and Yusuf [16] discussed the AB fractional order derivatives in the Caputo sense to analyze popular mathematical models involving two vaccines, not only simplifying the original ordinary differential equation model and matching the findings to the classical case, but also the fractional order model retains all memory effects, making the model a better match to the AB fractional order derivatives in the Caputo sense; Gupta and Kumar [17] developed an image denoising model using Caputo, Caputo-Fabrizio and AB fractionalorder integration to verify the effectiveness of the method compared to the traditional fractional-order model using multiple parameter simulation results; Abdullah and Huang [18] analyzed the application of AB derivatives in the Caputo sense to a fractional model for plant disease control. More applications can refer [19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Stability and existence of solutions to a class of Atangana-Baleanu-Caputo coupled fractional differential equations

Lin

Wei-min

et al. 2023

Preprint

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In this paper, we are concerned with the stability and existence of solutions to a class of Atangana-Baleanu-Caputo coupled fractional differential equations. The existence and uniqueness of the solution of the fractional system are obtained through Schaefer and Banach fixed point theorems, and sufficient conditions for the existence and uniqueness of the solutions are also developed. Subsequently, the Hyers-Ulam stability and generalized Hyers-Ulam stability of the solution are considered. In particular, two examples are given to illustrate the main results. The interesting aspect of this paper is that it performs numerical simulations using the monotone iterative method to verify the applicability of the system.

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Generalized framework for the design of adaptive fractional-order masks for image denoising

Cited by 15 publications

References 38 publications

Depth Image Enhancement Algorithm Based on Fractional Differentiation

Depth Image Enhancement Algorithm Based on Fractional Differentiation

Optimization of parameters for image denoising algorithm pertaining to Generalized Caputo-Febrizio Fractional Operator

Stability and existence of solutions to a class of Atangana-Baleanu-Caputo coupled fractional differential equations

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