A Gray Level Indicator-Based Regularized Telegraph Diffusion Model: Application to Image Despeckling

Majee, Sudeb; Ray, Rajendra K.; Majee, Ananta K.

doi:10.1137/19m1283033

Cited by 12 publications

(9 citation statements)

References 41 publications

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“…The literature [8] gives an image diffusion model, which reflects the complexity of image texture with the help of local variance of the image, and also introduces fractional order in the model. In the literature [9], an adaptive fractional-order image edge detection model is proposed to improve the PM model, which introduces fractional-order and fidelity terms, both of which will greatly improve the situation of "step effect" in the PM model and also reduce the running time of the algorithm model and remove the noise in the image while preserving. It also reduces the running time of the algorithm model and removes the noise from the image while preserving most of the texture in the image.…”

Section: Related Studiesmentioning

confidence: 99%

Fractional-Order Adaptive $P$ -Laplace Equation-Based Art Image Edge Detection

Chen

2021

Advances in Mathematical Physics

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In recent years, with the rapid development of image processing research, the study of nonstandard images has gradually become a research hotspot, for example, fabric images, remote sensing images, and gear images. Some of the remote sensing images have a complex background and low illumination compared with standard images and are easy to be mixed with noise during acquisition; some of the fabric images have rich texture information, which adds difficulty to the related processing, and are also easy to be mixed with noise during acquisition. In this paper, we propose a fractional-order adaptive P -Laplace equation image edge detection algorithm for the problem of image edge detection in which the edge and texture information of the image is lost. The algorithm can apply for the order adaptively to filter the noise according to the noise distribution of the image, and the adaptive diffusion factor is determined by both the fractional-order curvature and fractional-order gradient of the iso-illumination line and combined with the iterative approach to realize the fine-tuning of the noisy image. The experimental results demonstrate that the algorithm can remove the noise while preserving the texture and details of the image. A fractional-order partial differential equation image edge detection model with a fractional-order fidelity term is proposed for Gaussian noise. The model incorporates a fractional-order fidelity term because this fidelity term smoothes out the rougher parts of the image while preserving the texture in the original image in greater detail and eliminating the step effect produced by other models such as the Perona-Malik (PM) and Rudin-Osher-Fatemi (ROF) models. By comparing with other algorithms, the image edge detection effect is measured with the help of evaluation metrics such as peak signal-to-noise ratio and structural similarity, and the optimal value is selected iteratively so that the image with the best edge detection result is retained. A convolutional mask image edge detection model based on adaptive fractional-order calculus is proposed for the scattered noise in medical images. The adaption is mainly reflected in the model algorithm by constructing an exponential parameter relation that is closely related to the image, which can dynamically adjust the parameter values, thus making the model algorithm more practical. The model achieves the scattering noise removal in four steps.

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Section: Related Studiesmentioning

confidence: 99%

Fractional-Order Adaptive $P$ -Laplace Equation-Based Art Image Edge Detection

Chen

2021

Advances in Mathematical Physics

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“…Then, Liu et al 17 proposed a new model using a fractional reaction‐diffusion system for image restoration and image decomposition, they decomposed the degraded image into cartoon component belonging to a fractional Sobolev space and textured component belonging to a negative Hilbert space, and they proved the existence and uniqueness of weak solutions of their model by a regularization method. Recently, Majee et al 18 proposed a gray level indicator‐based nonlinear telegraph diffusion system for image despeckling. Moreover, they proved the well‐posedness of the present system by using the Schauder's fixed point theorem.…”

Section: Introductionmentioning

confidence: 99%

A novel fractional‐order reaction diffusion system for the multiplicative noise removal

et al. 2021

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In this paper, a fractional‐order nonlinear reaction diffusion system is proposed to remove the multiplicative Gamma noise. The new reaction diffusion system consists of three equations: the regularized Perona and Malik (PM) equation , which is used for presmoothing the image that is contaminated by noise; the time‐delay regularization equation, which is used for incorporating the past information into the diffusion process and adjusting oversmoothing; and the fractional‐order diffusion equation, which is used for removing the multiplicative Gamma noise and maintaining texture. The new reaction diffusion system is coupled, leading to the difficulty in theoretical analysis. To this end, we use decoupled and Schauder's fixed‐point theorem to obtain the existence and uniqueness of weak solution of the system. The explicit finite difference scheme is employed to implement the fractional‐order nonlinear reaction diffusion system. In addition, we test both texture images and nontexture images. Experimental results show that the new model achieves a better trade‐off between denoising performance and texture preservation than the other three models.

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“…• Since the proposed model consists of the telegraph equation [42,47], it could enhance the detect edges better than the diffusion-based approaches in the noise removal process. In the existing literature, the telegraph total variation based technique has been used only to remove the additive Gaussian noise.…”

mentioning

confidence: 99%

“…Despite their attention in the area of additive noise elimination, the telegraph equation based technique has not been paid so much attention for the multiplicative speckle noise removal. Recently Majee et al [42] proposed a gray level indicator-based telegraph-diffusion model for image despeckling. The model in [42] takes the form (4)…”

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A fuzzy edge detector driven telegraph total variation model for image despeckling

Majee¹,

Jain²,

Ray³

et al. 2022

IPI

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<p style='text-indent:20px;'>Speckle noise suppression is a challenging and crucial pre-processing stage for higher-level image analysis. In this work, a new attempt has been made using telegraph total variation equation and fuzzy set theory for image despeckling. The intuitionistic fuzzy divergence function has been used to distinguish between edges and noise. To the best of the authors' knowledge, most of the studies on the multiplicative speckle noise removal process focus only on diffusion-based filters, and little attention has been paid to the study of fuzzy set theory. The proposed approach enjoys the benefits of both telegraph total variation equation and fuzzy edge detector, which is robust to noise and preserves image structural details. Moreover, we establish the existence and uniqueness of weak solutions of a regularized version of the present system using the Schauder fixed point theorem. With the proposed technique, despeckling is carried out on natural, real synthetic aperture radar, and real ultrasound images. The experimental results computed by the suggested method are reported, which are found better in terms of noise elimination and detail/edge preservation, concerning the existing approaches.</p>

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A Gray Level Indicator-Based Regularized Telegraph Diffusion Model: Application to Image Despeckling

Cited by 12 publications

References 41 publications

Fractional-Order Adaptive $P$ -Laplace Equation-Based Art Image Edge Detection

Fractional-Order Adaptive $P$ -Laplace Equation-Based Art Image Edge Detection

A novel fractional‐order reaction diffusion system for the multiplicative noise removal

A fuzzy edge detector driven telegraph total variation model for image despeckling

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A Gray Level Indicator-Based Regularized Telegraph Diffusion Model: Application to Image Despeckling

Cited by 12 publications

References 41 publications

Fractional-Order Adaptive P -Laplace Equation-Based Art Image Edge Detection

Fractional-Order Adaptive P -Laplace Equation-Based Art Image Edge Detection

A novel fractional‐order reaction diffusion system for the multiplicative noise removal

A fuzzy edge detector driven telegraph total variation model for image despeckling

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Fractional-Order Adaptive $P$ -Laplace Equation-Based Art Image Edge Detection

Fractional-Order Adaptive $P$ -Laplace Equation-Based Art Image Edge Detection