Fractional nonlinear anisotropic diffusion with p-Laplace variation method for image restoration

Yin, Xuehui; Zhou, Shangbo; Siddique, Muhammad Abubakar

doi:10.1007/s11042-015-2488-6

Cited by 25 publications

(6 citation statements)

References 27 publications

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“…A novel class of fractional-order nonlinear anisotropic diffusion equations based image restoration model is established employing the p-Laplace norm of fractional-order gradient of an image intensity function is introduced in another paper where fractional-order gradient helps to better accommodate the images texture details. Thus, the proposed method removed noise and kept high-frequency edge of images in an efficient way nonlinearly (Yin et al 2015). Another research provides a novel fast fractional order anisotropic diffusion algorithm to remove noise removal.…”

Section: Chaosmentioning

confidence: 99%

A New Fractional-order Derivative-based Nonlinear Anisotropic Diffusion Model for Biomedical Imaging

CHAUHAN,

KUMAR,

KARACA

2023

Chaos Theory and Applications

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Nonlinear anisotropic diffusion equations are employed to ensure the improvement of the image quality by removing noise while retaining the subtle details and edges. Image denoising is observed to be of utmost importance in image processing and computer vision to prepare the images with better resolutions. Partial differential equations (PDEs), in this sense, can be used extensively in different aspects with regard to image processing ranging from filtering to restoration, segmentation to edge enhancement and detection, denoising in particular, among the other ones. The medical images (ultrasound images, X-rays, CT scans, MRIs, etc.) may lose significant features and become degraded due to the emergence of noise. As a result, the process of improvement pertaining to medical images has become a thought-provoking area of inquiry with challenges related to detecting the additive noise in the images and finding the applicable solution in a timely manner. To this end, numerous denoising techniques have been established. In this research paper, we present a conformable fractional derivative-based anisotropic diffusion model for removing speckle noise in ultrasound images. Chaos, as a ubiquitous phenomenon in nature, manifests the fact that the observed chaotic and noisy signals are often disrupted by external interferences. Edge, as one of the most remarkable features for images, requires denoising via nonlinear means to attain optimal outcomes. The finite difference method is used to discretize the fractional diffusion model and classical diffusion models. The peak signal-to-noise ratio (PSNR) is used for the quality of the smooth images. The aim of this study is to prove the viscosity solution of the diffusion model with the proposed model providing to be efficient in reducing noise by preserving the essential image features like edges, corners and other sharp structures for ultrasound images in comparison to the classical anisotropic diffusion model. Comparative experimental results corroborate that the proposed and extended mathematical model is capable of denoising and preserving the significant features in ultrasound within the framework of biomedical imaging and other related medical, clinical and image-signal related applied as well as computational processes.

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Section: Chaosmentioning

confidence: 99%

A New Fractional-order Derivative-based Nonlinear Anisotropic Diffusion Model for Biomedical Imaging

CHAUHAN,

KUMAR,

KARACA

2023

Chaos Theory and Applications

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“…Therefore, other detection operators are selected to make the model parameters adaptive 24 – 29 Among them, a structure tensor matrix can depict the gradient and edge direction information precisely for the consistency of direction and measurement provided by its eigenvalues and eigenvectors, so it can be used to detect the edge and texture of images 23 , 30 – 33 In addition, the structure tensor matrix is a very practical image local structure analysis tool to detect corners and edge direction in the field of computer vision and image processing, including optical flow estimation, 34 corner detector, 34 , 35 analysis of persistent motion, 36 image interpolation, 37 image regularization, 38 and image enhancement 39 …”

Section: Introductionmentioning

confidence: 99%

Image denoising model using adaptive regularization parameter based on structure tensor

Zhao,

Zhao

2024

J. Electron. Imag.

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The denoising method based on partial differential equation (PDE) has been proven to be a calculable method and used widely, but it is not good at protecting image detail information and results in staircase effect. To improve the above shortcomings, a PDE image denoising model based on a structure tensor matrix is proposed and explained in this work. Combining two different regular terms and adjusting their proportion, the proposed model uses the eigenvalues of the structure tensor to take the norm parameter value of the second regular term. The experiment results show that the proposed model introduced structure tensor can protect details and suppress the staircase effect effectively, thus obtaining satisfying denoising results.

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“…However, the main interest rests in concrete applications, since anisotropic media naturally arise in several real world phenomena. In fact, anisotropic energies are widely used in computer vision (see for instance [1,13,20,28,29]) and in continuum mechanics, in particular in presence of materials with distinct behavior with respect to different directions, typically due to the crystalline microstructure of the medium (see for instance [3,4,6,7,15,25] and the references therein). Our main results are a Hopf Lemma at the boundary, as well as local and global regularity estimates for positive solutions Let us remark that, in a forthcoming paper, as a direct application of the results discussed above, we shall develop a moving plane procedure in the general context of this anisotropic and possibly singular/degenerate elliptic equations, in order to prove monotonicity and symmetry results in this Finsler geometry setting for positive solutions, both on bounded and unbounded domains, such as the whole space R n or on half spaces.…”

Section: Introductionmentioning

confidence: 99%

Hopf Lemma and regularity results for quasilinear anisotropic elliptic equations

2019

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Fractional nonlinear anisotropic diffusion with p-Laplace variation method for image restoration

Cited by 25 publications

References 27 publications

A New Fractional-order Derivative-based Nonlinear Anisotropic Diffusion Model for Biomedical Imaging

A New Fractional-order Derivative-based Nonlinear Anisotropic Diffusion Model for Biomedical Imaging

Image denoising model using adaptive regularization parameter based on structure tensor

Hopf Lemma and regularity results for quasilinear anisotropic elliptic equations

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