<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Image recovery is a class of ill-posed inverse problems, so image recovery has been a challenging and fundamental topic in image processing. In this paper, firstly, to recover blurred images with noise, an adaptive fully variable partial differential image recovery model is proposed based on the fully variable partial differential equation model and Gaussian thermal diffusion model, where the adaptiveness is achieved logarithmically by regularizing the edge detection operator. Secondly, a finite difference method, which covers the gradient and scatters operators in the partial differential equation, is applied to the problem of fixing the global range boundary conditions of the image. Finally, the gradient of the image is restored, and then the gradient domain of the image is solved to obtain the complete recovered image. The results show that in the evaluation of the image restoration effect aspect by two indexes, PSNR and SSIM, the value of the adaptive fully variable partial differential image restoration model increases from 28 to 32, and the value of SSIM increases from 0.70 to 0.88, which has good image restoration performance. The adaptive fully variable partial differential image restoration model proposed in this paper has the characteristics of good edge protection and fast convergence, which is of guiding significance for the numerical implementation of image restoration techniques.</p>
</abstract>

Image recovery is a class of ill-posed inverse problems, so image recovery has been a challenging and fundamental topic in image processing. In this paper, firstly, to recover blurred images with noise, an adaptive fully variable partial differential image recovery model is proposed based on the fully variable partial differential equation model and Gaussian thermal diffusion model, where the adaptiveness is achieved logarithmically by regularizing the edge detection operator. Secondly, a finite difference method, which covers the gradient and scatters operators in the partial differential equation, is applied to the problem of fixing the global range boundary conditions of the image. Finally, the gradient of the image is restored, and then the gradient domain of the image is solved to obtain the complete recovered image. The results show that in the evaluation of the image restoration effect aspect by two indexes, PSNR and SSIM, the value of the adaptive fully variable partial differential image restoration model increases from 28 to 32, and the value of SSIM increases from 0.70 to 0.88, which has good image restoration performance. The adaptive fully variable partial differential image restoration model proposed in this paper has the characteristics of good edge protection and fast convergence, which is of guiding significance for the numerical implementation of image restoration techniques.

Numerical implementation of level set image recovery based on partial differential equation model

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Image recovery is a class of ill-posed inverse problems, so image recovery has been a challenging and fundamental topic in image processing. In this paper,...

Numerical implementation of level set image recovery based on partial differential equation model

Published Online: Sep 06, 2023

Page range: -

Received: Dec 12, 2022

Accepted: Mar 17, 2022

DOI: https://doi.org/10.2478/amns.2023.2.00294

Keywords
Image restoration, Partial differential equation model, Boundary conditions, Finite difference method, Gradient domain

© 2023 Xiang Liu, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Numerical implementation of level set image recovery based on partial differential equation model

Published Online: Sep 06, 2023

Page range: -

Received: Dec 12, 2022

Accepted: Mar 17, 2022

DOI: https://doi.org/10.2478/amns.2023.2.00294

KeywordsImage restoration, Partial differential equation model, Boundary conditions, Finite difference method, Gradient domain

© 2023 Xiang Liu, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Image restoration, Partial differential equation model, Boundary conditions, Finite difference method, Gradient domain