On a partial differential equation method for determining the free energies and coexisting phase compositions of ternary mixtures from light scattering data

2008 ◽  
Vol 129 (6) ◽  
pp. 064106 ◽  
Author(s):  
David S. Ross ◽  
George M. Thurston ◽  
Carl V. Lutzer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Light Scattering ◽  
Ternary Mixtures ◽  
Equation Method ◽  
Scattering Data ◽  
Free Energies ◽  
Partial Differential ◽  
Differential Equation Method

scholarly journals Partial Differential Equations-Based Iterative Denoising Algorithm for Movie Images

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Pingli Sun ◽  
Chenxia Wang ◽  
Min Li ◽  
Lanqi Liu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Noise Reduction ◽  
Video Processing ◽  
Gaussian Noise ◽  
Video Image ◽  
Equation Method ◽  
Partial Differential ◽  
Iterative Denoising ◽  
Differential Equation Method

Film video noise can usually be defined as the error information visible on the video image, caused by the digital signal system. This distortion is inevitably present in the video obtained by various camera equipment. Noise reduction techniques are important preprocessing processes in many video processing applications, and its main goal is to reduce the noise contained in a video image while preserving as much of its edge and texture information as possible. In this paper, we describe in detail the principles of the space-time noise reduction filter, propose a 3D-filter algorithm for Gaussian noise, an improved 3D-filter algorithm based on the 3D-BDP (bloom-deep-split) filter for mixed noise, and a filter algorithm for luminance and color noise in low-brightness scenes. By dissecting the partial differential equation (PDE) denoising process, we establish a new iterative denoising algorithm. The partial differential equation method can be considered as the iterative denoising of the filter, and the first stage of the new algorithm uses wavelet-domain adaptive Wiener filter as the filtering base and achieves good results by adjusting the parameters. The proposed model in this paper is compared with the existing denoising model, and the analysis results show that the model proposed in this section can effectively remove multiplicative noise. The experimental report shows that the parameters set by the algorithm have some stability and can achieve good processing results for multiple images, which is an advantage over the partial differential equation method for denoising. The second stage of the algorithm uses the appropriate partial differential equation method to remove the pseudo-Gibbs in the first stage, which further improves the performance of the algorithm. After the image containing Gaussian noise is processed by the new algorithm, the pseudo-Gibbs effect, which often occurs in wavelet denoising, is eliminated, and the step effect, which occurs in partial differential equation denoising, is avoided; the details are better preserved, and the peak signal-to-noise ratio is improved, and a large number of experiments show that it is an effective denoising method.

scholarly journals Automatic Recognition Method of Letter Images in English Self-Learning Based on Partial Differential Equation Method

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yu Zhao ◽  
Shuping Du ◽  
Ran Li ◽  
Hong Yue
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Equation Method ◽  
Initial Contour ◽  
Partial Differential ◽  
Image Gradient ◽  
Curvature Motion ◽  
Differential Equation Method

According to the current situation of knowledge popularization, students simply rely on the knowledge learned in the classroom that is far from adapting to the development of modern society; so, every student needs to have the consciousness and ability of independent learning. The research of the English self-help learning system based on partial differential equation method comes into being with information network technology as the foundation for survival and development. The existing partial differential equation recognition models based on average curvature motion are all edge-based and need to use the external force defined by the image gradient to attract the zero level set (evolution curve) to move to the target edge and finally stay on the target edge. Therefore, it is difficult to obtain ideal results when extracting fuzzy or discrete boundaries (perceptual boundaries), and it is very sensitive to the selection of initial contour and noise. To solve this problem, this paper proposes a new recognition model of partial differential equations based on mean curvature motion. This overcomes some defects of existing edge models because it is region-based and does not require image gradient as a condition to stop evolution. The proposed model can avoid manual initial curve selection and allow stopping conditions to be set in the algorithm. In addition, in the numerical solution of partial differential equations, the existing model uses upwind difference scheme, and the semi-implicit additive operator separation method is adopted in this paper. Some other layers are added, and some hyperparameters are adjusted when the convolutional neural networks of inception PDEs are constructed by stacking the structure of inception PDEs. In the contrast experiment with the prototype, the software and hardware environment are the same, and the input is exactly the same. For the handwritten English alphabet data set, the variant structure can obtain more than 90% of the training accuracy and verification accuracy, which is better than the experimental accuracy of the prototype. In addition, because the inception PDE structure contains fewer parameters than the prototype, it is more computationally efficient and takes less training time per batch than the prototype.

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