Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising
The partial differential equation (PDE)-based models are widely used to remove additive Gaussian white noise and preserve edges, and one of the most widely used methods is the total variation denoising algorithm. Total variation (TV) denoising algorithm-based time-dependent models have seen consider...
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Akif AKGUL
2023-12-01
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| Series: | Chaos Theory and Applications |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3251030 |
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| author | Khursheed Alam Alka Chauhan Santosh Kumar |
| author_facet | Khursheed Alam Alka Chauhan Santosh Kumar |
| author_sort | Khursheed Alam |
| collection | DOAJ |
| description | The partial differential equation (PDE)-based models are widely used to remove additive Gaussian white noise and preserve edges, and one of the most widely used methods is the total variation denoising algorithm. Total variation (TV) denoising algorithm-based time-dependent models have seen considerable success in the field of image-denoising and edge detection. TV denoising algorithm is based on that signals with spurious detail have a high total variation and reduction of unwanted signals to achieve noise-free images. It is a constrained optimization-type algorithm. The Lagrange multiplier and gradient descent method are used to solve the TV algorithm to reach the PDE-based time dependent model. To eliminate additive noise and preserve edges, we investigate a class of weighted time-dependent model in this study. The proposed method is investigated in a well-balanced flow form that extends the time-dependent model with an adaptive fidelity element. Adaptive function is fusing into the regularization term of the classical time-dependent model which successfully enhances the intensity of the regularizer function. We maintain the ability of the time-dependent model without any oscillation effects. Furthermore, we want to prove the viscosity solution of our weighted and well balanced time-dependent model, demonstrating its existence and uniqueness. The finite difference method is applied to discretize the nonlinear time-dependent models. The numerical results are expressed as a statistic known as the peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM). Numerical experiments demonstrate that the proposed model yields good performance compared with the previous time-dependent model. |
| format | Article |
| id | doaj-art-d2f51c89e55241e4b62c2739e322dc16 |
| institution | Kabale University |
| issn | 2687-4539 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Akif AKGUL |
| record_format | Article |
| series | Chaos Theory and Applications |
| spelling | doaj-art-d2f51c89e55241e4b62c2739e322dc162025-01-23T18:15:39ZengAkif AKGULChaos Theory and Applications2687-45392023-12-015430030710.51537/chaos.13243551971Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image DenoisingKhursheed Alam0https://orcid.org/0000-0003-4168-3736Alka Chauhan1https://orcid.org/0009-0002-2957-4916Santosh Kumar2https://orcid.org/0000-0001-9500-7229Sharda University Greater NoidaSharda University Greater NoidaSharda University Greater NoidaThe partial differential equation (PDE)-based models are widely used to remove additive Gaussian white noise and preserve edges, and one of the most widely used methods is the total variation denoising algorithm. Total variation (TV) denoising algorithm-based time-dependent models have seen considerable success in the field of image-denoising and edge detection. TV denoising algorithm is based on that signals with spurious detail have a high total variation and reduction of unwanted signals to achieve noise-free images. It is a constrained optimization-type algorithm. The Lagrange multiplier and gradient descent method are used to solve the TV algorithm to reach the PDE-based time dependent model. To eliminate additive noise and preserve edges, we investigate a class of weighted time-dependent model in this study. The proposed method is investigated in a well-balanced flow form that extends the time-dependent model with an adaptive fidelity element. Adaptive function is fusing into the regularization term of the classical time-dependent model which successfully enhances the intensity of the regularizer function. We maintain the ability of the time-dependent model without any oscillation effects. Furthermore, we want to prove the viscosity solution of our weighted and well balanced time-dependent model, demonstrating its existence and uniqueness. The finite difference method is applied to discretize the nonlinear time-dependent models. The numerical results are expressed as a statistic known as the peak signal-to-noise ratio (PSNR) and structural similarity index metric (SSIM). Numerical experiments demonstrate that the proposed model yields good performance compared with the previous time-dependent model.https://dergipark.org.tr/en/download/article-file/3251030partial differentialequationtotal variationtime dependentmodelweighted andwell balancedimage denoisingimage smoothingviscosity solutionexplicit scheme |
| spellingShingle | Khursheed Alam Alka Chauhan Santosh Kumar Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising Chaos Theory and Applications partial differentialequation total variation time dependentmodel weighted andwell balanced image denoising image smoothing viscosity solution explicit scheme |
| title | Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising |
| title_full | Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising |
| title_fullStr | Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising |
| title_full_unstemmed | Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising |
| title_short | Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising |
| title_sort | weighted and well balanced nonlinear tv based time dependent model for image denoising |
| topic | partial differentialequation total variation time dependentmodel weighted andwell balanced image denoising image smoothing viscosity solution explicit scheme |
| url | https://dergipark.org.tr/en/download/article-file/3251030 |
| work_keys_str_mv | AT khursheedalam weightedandwellbalancednonlineartvbasedtimedependentmodelforimagedenoising AT alkachauhan weightedandwellbalancednonlineartvbasedtimedependentmodelforimagedenoising AT santoshkumar weightedandwellbalancednonlineartvbasedtimedependentmodelforimagedenoising |