Image decomposition and denoising using fractional‐order partial differential equations

Bai, Jian; Feng, Xiaoyi

doi:10.1049/iet-ipr.2018.5499

Cited by 11 publications

(5 citation statements)

References 36 publications

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“…The difference between the two is not big. In the wavelet multiscale analysis theory, we often use wavelet coefficients' amplitude to measure the function's regularity [8]. The Lipschitz exponent j  of each scale part of the function ( , ) f x y is estimated as follows:…”

Section: The Choice Of Sobolev Space Index J Smentioning

confidence: 99%

Fractional Differential Equations in Electronic Information Models

Lei

Shatat

Lakys

2023

Applied Mathematics and Nonlinear Sciences

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The article first uses the fractional derivative to define a new fractional bounded variation function space. This method constructs the corresponding electronic information image model denoising mask by setting a smaller fractional integration order. The experimental results show that the image denoising algorithm based on fractional integration can not only improve the signal-to-noise ratio of the image compared with the traditional denoising method, but also can better retain the details of the edge and texture of the electronic information image.

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Section: The Choice Of Sobolev Space Index J Smentioning

confidence: 99%

Fractional Differential Equations in Electronic Information Models

Lei

Shatat

Lakys

2023

Applied Mathematics and Nonlinear Sciences

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“…In 1990, the nonlinear diffusion P-M model for additive noise removal proposed by Perona and Malik needs to introduce the gradient information of the image into the diffusion coefficient in order to maintain the edge while denoising. [3] However, due to the negative characteristic of the diffusion coefficient in a certain direction, the model is required to be regular in space and time. Its model is:…”

Section: Image Denoising Model Based On Pdementioning

confidence: 99%

Image denoising model based on improved fractional calculus mathematical equation

Wang

2022

Applied Mathematics and Nonlinear Sciences

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Aiming at the problems of image edge blur and detail loss in most image denoising models, an image denoising model based on improved fractional calculus is proposed. Through the classification of image noise, the integer order PDE model is discussed. Based on the mathematical theory of fractional calculus, the fractional PDE model is discussed. The model is improved by combining texture detection operator, gray value detection operator, smoothing factor and fast algorithm. The simulation experiment of the model is carried out based on MATLAB simulation platform. The results show that the improved model is significantly better than other comparison models in image denoising effect, and the operation efficiency is higher.

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“…Fractional order calculation has been applied for different image processing fields [14][15][16]. It is noted that fractional differential is the differential calculation with a non-integral order.…”

Section: Introductionmentioning

confidence: 99%

Adaptive fractional differential algorithm for image edge enhancement and texture preserve using fuzzy sets

Li¹,

Xie

Zhang

et al. 2023

IET Image Processing

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This paper uses a fuzzy set scheme to present an adaptive fractional differential algorithm for image edge enhancement and texture preservation. In the proposed algorithm, an image's membership function and area feature are used to calculate the fuzzy set of images. The function of adaptive fractional differential order (FAFDO) can be constructed by making the linear transformation of the fuzzy set. Then, the fuzzy adaptive fractional differential mask (FAFDM) is obtained by substituting the FAFDO into the fractional differential mask. Finally, the image edge and texture are enhanced and preserved by applying airspace filtering of the FAFDM convolution. The experimental results show that, compared to fractional differential or fuzzy set‐based image enhancement algorithms, the proposed algorithm can adaptively enhance the image edge and preserve the image texture by analysing the fuzziness of the image itself.

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Image decomposition and denoising using fractional‐order partial differential equations

Cited by 11 publications

References 36 publications

Fractional Differential Equations in Electronic Information Models

Fractional Differential Equations in Electronic Information Models

Image denoising model based on improved fractional calculus mathematical equation

Adaptive fractional differential algorithm for image edge enhancement and texture preserve using fuzzy sets

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