scholarly journals A Partial Differential Equation-Based Image Restoration Method in Environmental Art Design

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Chen Li
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Image Restoration ◽  
Rapid Development ◽  
Real Life ◽  
Generative Adversarial Networks ◽  
Environmental Art ◽  
Partial Differential ◽  
Art Design ◽  
Restoration Model

With the rapid development of networks and the emergence of various devices, images have become the main form of information transmission in real life. Image restoration, as an important branch of image processing, can be applied to real-life situations such as pixel loss in image transmission or network prone to packet loss. However, existing image restoration algorithms have disadvantages such as fuzzy restoration effect and slow speed; to solve such problems, this paper adopts a dual discriminator model based on generative adversarial networks, which effectively improves the restoration accuracy by adding local discriminators to track the information of local missing regions of images. However, the model is not optimistic in generating reasonable semantic information, and for this reason, a partial differential equation-based image restoration model is proposed. A classifier and a feature extraction network are added to the dual discriminator model to provide category, style, and content loss constraints to the generative network, respectively. To address the training instability problem of discriminator design, spectral normalization is introduced to the discriminator design. Extensive experiments are conducted on a data dataset of partial differential equations, and the results show that the partial differential equation-based image restoration model provides significant improvements in image restoration over previous methods and that image restoration techniques are exceptionally important in the application of environmental art design.

An Efficient Image Segmentation Using Partial Differential Equation for Image Processing Applications

2021 ◽  
Vol 11 (10) ◽  
pp. 2538-2545
Author(s):  
P. Geetha ◽  
S. Nagarani
Keyword(s):  
Differential Equation ◽  
Mathematical Method ◽  
Image Processing ◽  
Partial Differential Equation ◽  
Image Segmentation ◽  
Image Restoration ◽  
Geometric Analysis ◽  
Stochastic Modelling ◽  
Partial Differential ◽  
Structural Work

Different processing of the images, such as the image captured, saved and retrieved from another use of the specific image, must be restructured in various ways in the process. More methods such as image restoration, picture segmentation, improvement of the picture etc can be used when processing images. Reconstructed in 3D picture 2D pictures are need to be proper. Including geometric wavelets and geometric analysis the structural work focused upon a variational and a selectable differential equation to test PDE’s which is a convergence of stochastic modelling and analysis of harmonics. This paper focuses primarily on the critical reviews of the image segmentation collection with the PDE application as a mathematical method and introduces the key tool of mathematics and techniques along with the literature-based analysis.

Adaptive Fourth Order Partial Differential Equation Filter from the Webers Total Variation for Image Restoration

2013 ◽  
Vol 475-476 ◽  
pp. 394-400
Author(s):  
Dong Hong Zhao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Diffusion Equation ◽  
Image Restoration ◽  
Total Variation ◽  
Laplace Operator ◽  
Fourth Order ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Directed Diffusion

By substituting an anisotropic diffusion operator for the isotropic Laplace operator in the directed diffusion equation, an improvd directed diffusion equation model is proposed. To overcome the staircasing effects and simultaneously avoid edge blurring, this paper proposed an adaptive fourth order partial differential equation from the Webers Total Variation for Image Restoration. This functional is not only to use Laplace operator but also to add the human psychology system, this paper show numerical evidence of the power of resolution of the model with respect to other known models as the Perona-Malik model. Compared results disctincly demonstrate the superiority of our proposed scheme , in terms of removing noise while sharply maintaining the edge features.

scholarly journals Stochastic Seismic Waveform Inversion Using Generative Adversarial Networks as a Geological Prior

2019 ◽  
Vol 52 (1) ◽  
pp. 53-79 ◽  
Author(s):  
Lukas Mosser ◽  
Olivier Dubrule ◽  
Martin J. Blunt
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Latent Variables ◽  
Generative Models ◽  
Generative Model ◽  
Generative Adversarial Networks ◽  
Bayesian Inversion ◽  
Model Parameters ◽  
Partial Differential ◽  
Seismic Waveform

AbstractWe present an application of deep generative models in the context of partial differential equation constrained inverse problems. We combine a generative adversarial network representing an a priori model that generates geological heterogeneities and their petrophysical properties, with the numerical solution of the partial-differential equation governing the propagation of acoustic waves within the earth’s interior. We perform Bayesian inversion using an approximate Metropolis-adjusted Langevin algorithm to sample from the posterior distribution of earth models given seismic observations. Gradients with respect to the model parameters governing the forward problem are obtained by solving the adjoint of the acoustic wave equation. Gradients of the mismatch with respect to the latent variables are obtained by leveraging the differentiable nature of the deep neural network used to represent the generative model. We show that approximate Metropolis-adjusted Langevin sampling allows an efficient Bayesian inversion of model parameters obtained from a prior represented by a deep generative model, obtaining a diverse set of realizations that reflect the observed seismic response.

A Partial Differential Equation Algorithm for Image Denoising

2013 ◽  
Vol 816-817 ◽  
pp. 554-556
Author(s):  
Min Ma ◽  
Liang Zhao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Image Restoration ◽  
Image Denoising ◽  
Anisotropic Diffusion ◽  
Image Inpainting ◽  
Partial Differential ◽  
Simulation Results ◽  
Different Levels

Image restoration is necessary in many applications as the captured images are inevitably noise-contaminated. Typically, the partical differential equations based methods, which is a primary class of image inpainting techniques, is well accepted. In this paper,anisotropic diffusion (P-M) model was introduced to image denoisng. Simulation results were implemented of the proposed method by using Matlab, in which different levels of noise were compared to show the advantages and the disadvantages.

scholarly journals Noise Data Removal and Image Restoration Based on Partial Differential Equation in Sports Image Recognition Technology

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Shi Junmei
Keyword(s):  
Differential Equation ◽  
Image Processing ◽  
Partial Differential Equation ◽  
Image Restoration ◽  
Image Recognition ◽  
Image Data ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Image Information ◽  
Noise Data

With the rapid development of image processing technology, the application range of image recognition technology is becoming more and more extensive. Processing, analyzing, and repairing graphics and images through computer and big data technology are the main methods to obtain image data and repair image data in complex environment. Facing the low quality of image information in the process of sports, this paper proposes to remove the noise data and repair the image based on the partial differential equation system in image recognition technology. Firstly, image recognition technology is used to track and obtain the image information in the process of sports, and the fourth-order partial differential equation is used to optimize and process the image. Finally, aiming at the problem of low image quality and blur in the transmission process, denoising is carried out, and image restoration is studied by using the adaptive diffusion function in partial differential equation. The results show that the research content of this paper greatly improves the problems of blurred image and poor quality in the process of sports and realizes the function of automatically tracking the target of sports image. In the image restoration link, it can achieve the standard repair effect and reduce the repair time. The research content of this paper is effective and applicable to image processing and restoration.

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