scholarly journals Adaptive Image Denoising Method Based on Diffusion Equation and Deep Learning

2022 ◽  
Vol 2022 ◽  
pp. 1-9
Author(s):  
Shaobin Ma ◽  
Lan Li ◽  
Chengwen Zhang
Keyword(s):  
Diffusion Coefficient ◽  
Deep Learning ◽  
Diffusion Equation ◽  
Image Denoising ◽  
Noise Removal ◽  
Learning Ability ◽  
Threshold Function ◽  
Extraction Technology ◽  
Residual Learning ◽  
Comparison Results

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.

scholarly journals Fault Diagnosis under Variable Working Conditions Based on STFT and Transfer Deep Residual Network

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Yan Du ◽  
Aiming Wang ◽  
Shuai Wang ◽  
Baomei He ◽  
Guoying Meng
Keyword(s):  
Deep Learning ◽  
Fault Diagnosis ◽  
Transfer Learning ◽  
Working Conditions ◽  
Classification Accuracy ◽  
Working Condition ◽  
Learning Ability ◽  
Residual Network ◽  
Time Frequency ◽  
Residual Learning

Fault diagnosis plays a very important role in ensuring the safe and reliable operations of machines. Currently, the deep learning-based fault diagnosis is attracting increasing attention. However, fault diagnosis under variable working conditions has been a significant challenge due to the domain discrepancy problem. This problem is also unavoidable in deep learning-based fault diagnosis methods. This paper contributes to the ongoing investigation by proposing a new approach for the fault diagnosis under variable working conditions based on STFT and transfer deep residual network (TDRN). The STFT was employed to convert vibration signal to time-frequency image as the input of the TDRN. To address the domain discrepancy problem, the TDRN was developed in this paper. Unlike traditional deep convolutional neural network (DCNN) methods, by combining with transfer learning, the TDRN can make a bridge between two different working conditions, thereby using the knowledge learned from a working condition to achieve a high classification accuracy in another working condition. Moreover, since the residual learning is introducing, the TDRN can overcome the problems of training difficulty and performance degradation existing in traditional DCNN methods, thus further improving the classification accuracy. Experiments are conducted on the popular CWRU bearing dataset to validate the effectiveness and superiority of the proposed approach. The results show that the developed TDRN outperforms those methods without transfer learning and/or residual learning in terms of the accuracy and feature learning ability for the fault diagnosis under variable working conditions.

scholarly journals Dedicated breast computed tomography: Volume image denoising via a partial-diffusion equation based technique

2008 ◽  
Vol 35 (5) ◽  
pp. 1950-1958 ◽  
Author(s):  
Jessie Q. Xia ◽  
Joseph Y. Lo ◽  
Kai Yang ◽  
Carey E. Floyd ◽  
John M. Boone
Keyword(s):  
Computed Tomography ◽  
Diffusion Equation ◽  
Image Denoising ◽  
Breast Computed Tomography

scholarly journals Inverse problem for fractional diffusion equation

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Vu Tuan
Keyword(s):  
Inverse Problem ◽  
Diffusion Coefficient ◽  
Lower Bound ◽  
Diffusion Equation ◽  
Spectral Data ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
One Dimensional ◽  
Initial Distributions

AbstractWe prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.

scholarly journals On the Theory of Electron Diffusion in Electrostatic Fields in Gases

1974 ◽  
Vol 27 (2) ◽  
pp. 195 ◽  
Author(s):  
HR Skullerud
Keyword(s):  
Diffusion Coefficient ◽  
Boltzmann Equation ◽  
Diffusion Equation ◽  
Diffusion Tensor ◽  
Lateral Diffusion ◽  
Mean Square ◽  
Electrostatic Fields ◽  
The Mean ◽  
Lateral Diffusion Coefficient

The motion of electrons in a gas in the presence of large electron density gradients has been studied theoretically, starting from the two-term expansion of the Boltzmann equation. The effects of material boundaries have not been considered. An electron swarm released as a b-function in space and with an equilibrium energy distribution is found initially to develop as a spheroid with dimensions determined by the lateral diffusion coefficient. It subsequently passes through a stage involving a slowly decaying pear-shaped deformation, before ultimately becoming an ellipsoid with dimensions determined by the longitudinal and lateral components of the diffusion tensor. Numerical values cited in the literature for the long-term deviations from the mean square widths predicted by the diffusion equation have been found to be in error by factors of 10 or more.

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