Denoising Method Based on Wavelet Coefficients via Diffusion Equation

Kumar, Santosh; Sarfaraz, Mohd.; Ahmad, Mukhtar

doi:10.1007/s40995-017-0228-7

Cited by 6 publications

(5 citation statements)

References 17 publications

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“…In the case of two-dimensional images, the general processing method is to treat the pair diffusion as a uniform linear diffusion process; that is to say, the diffusion coefficients at all points of the image are the same. However, there are still loopholes in this diffusion equation [2], whose uniform diffusion makes it impossible to retain important details such as edges while removing noise. In view of the defects of the uniform diffusion characteristics of Gaussian filtering, it is natural to come up with an ideal method: reduce the diffusion at the edge of the image according to the prior information of the image, so as to remove the noise from the image and protect the information at the edge [3].…”

Section: Related Workmentioning

confidence: 99%

Adaptive Image Denoising Method Based on Diffusion Equation and Deep Learning

Shaobin

Lan

Zhang

2022

Journal of Robotics

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Effective noise removal has become a hot topic in image denoising research while preserving important details of an image. An adaptive threshold image denoising algorithm based on fitting diffusion is proposed. Firstly, the diffusion coefficient in the diffusion equation is improved, and the fitting diffusion coefficient is established to overcome the defects of texture detail loss and edge degradation caused by excessive diffusion intensity. Then, the threshold function is adaptively designed and improved so that it can automatically control the threshold of the function according to the maximum gray value of the image and the number of iterations, so as to further preserve the important details of the image such as edge and texture. A neural network is used to realize image denoising because of its good learning ability of image statistical characteristics, mainly by the diffusion equation and deep learning (CNN) algorithm as the foundation, focus on the effects of activation function of network optimization, using multiple feature extraction technology in-depth networks to study the characteristics of the input image richer, and how to better use the adaptive algorithm on the depth of diffusion equation and optimization backpropagation learning. The training speed of the model is accelerated and the convergence of the algorithm is improved. Combined with batch standardization and residual learning technology, the image denoising network model based on deep residual learning of the convolutional network is designed with better denoising performance. Finally, the algorithm is compared with other excellent denoising algorithms. From the comparison results, it can be seen that the improved denoising algorithm in this paper can also improve the detail restoration of denoised images without losing the sharpness. Moreover, it has better PSNR than other excellent denoising algorithms at different noise standard deviations. The PSNR of the new algorithm is greatly improved compared with the classical algorithm, which can effectively suppress the noise and protect the image edge and detail information.

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Section: Related Workmentioning

confidence: 99%

Adaptive Image Denoising Method Based on Diffusion Equation and Deep Learning

Shaobin

Lan

Zhang

2022

Journal of Robotics

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“…With the improvement of the wavelet theory, its application fields have become more and more extensive. In the field of image recognition, the application of the wavelet theory for image recognition has attracted the attention of many experts and scholars and has achieved very good results [10,11]. Valandar et al were a few of the earliest researchers engaged in the application of wavelet in signal processing.…”

Section: Related Workmentioning

confidence: 99%

Application of Image Recognition Algorithm Based on Partial Differential Equation and Wavelet Transform in the Intelligent Linkage System of Government Urban Public Management

2021

Advances in Mathematical Physics

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In the Internet age, social needs have become more diverse. The private sector has achieved great success in integrating resources to provide services to customers thanks to technological breakthroughs such as mobile Internet and big data, while the public sector has become even more dwarfed. The public sector urgently needs new theoretical support to integrate administrative resources more effectively, so as to provide the public with one-stop, holistic and seamless services as a whole. The “holistic governance” theory effectively responded to the abovementioned problems and gradually condensed the consensus of the academic and practical circles and became the most influential theory. The method of mathematical modeling is used to combine the improved wavelet domain Wiener filter and the comprehensive model of partial differential equations. This paper proposes an image recognition algorithm based on partial differential equations and wavelet transform. The algorithm uses weight coefficients to organically combine high-order partial differential equation models, retains the advantages of the second- and fourth-order partial differential recognition models, effectively improves the ability to maintain image edge detail information, and achieves better recognition results. This article starts with the description of the fragmentation of a street’s grassroots governance and sorts out the process of implementing overall governance with the “big linkage mechanism” as the main carrier. Due to the limitations of research ability and objective conditions, this article intercepts the “cross-section” of the big linkage mechanism in a certain street to demonstrate it and analyzes this “cross-section” more thoroughly. The experimental results of the data show that the image recognition algorithm based on partial differential equations and wavelet transform is effective and practical in the intelligent linkage system of the government urban public management.

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“…The image obtained by wavelet decomposition is a wavelet series, which is the result of a linear filtering. If the wavelet filter has a linear phase or generalized linear phase, it is possible to fully reconstruct the original image [13][14][15]. Thus, no orthogonal wavelet except for Haar wavelet boasts the capability of full reconstruction.…”

Section: Influence Of Orthogonality and Bi-orthogonality On Denoisingmentioning

confidence: 99%

Wavelet-Based Self-adaptive Hierarchical Thresholding Algorithm and Its Application in Image Denoising

Zhang¹,

Zhu²,

Lin³

2019

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This paper attempts to construct a suitable wavelet for image denoising based on wavelet thresholding algorithm. First, the author discussed how image thresholding is affected by the wavelet orthogonality and bi-orthogonality, the features of vanishing moments and the odd or even symmetry of the decomposition end filter. The discussion shows that the most desirable wavelet for image denoising is the biorthogonal wavelet, in which the decomposition end filter has zero point even symmetry, the low-pass decomposition enjoys a wide support interval, and the high-pass decomposition filter has a short support and attenuates fast. On this basis, three zero point even symmetric biorthogonal wavelets with different vanishing moment features were developed through the parametric construction of fixed-length tightly-supported (FLTS) biorthogonal wavelet, and a self-adaptive hierarchical thresholding algorithm was designed. The simulation results show that the developed wavelets have excellent denoising ability and enhance the images with rich details. Coupled with the self-adaptive hierarchical thresholding algorithm, these wavelets can effectively improve the image quality.

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Denoising Method Based on Wavelet Coefficients via Diffusion Equation

Cited by 6 publications

References 17 publications

Adaptive Image Denoising Method Based on Diffusion Equation and Deep Learning

Adaptive Image Denoising Method Based on Diffusion Equation and Deep Learning

Application of Image Recognition Algorithm Based on Partial Differential Equation and Wavelet Transform in the Intelligent Linkage System of Government Urban Public Management

Wavelet-Based Self-adaptive Hierarchical Thresholding Algorithm and Its Application in Image Denoising

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