Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 5 Sayı: 4, 300 - 307, 31.12.2023
https://doi.org/10.51537/chaos.1324355

Öz

Kaynakça

  • Álvarez, L., P.-L. Lions, and J.-M. Morel, 1992 Image selective smoothing and edge detection by nonlinear diffusion. ii. SIAM Journal on Numerical Analysis 29: 845–866.
  • Barcelos, C., M. Boaventura, and E. Silva, 2003 A well-balanced flow equation for noise removal and edge detection. IEEE Transactions on Image Processing 12: 751–763.
  • Barcelos, C. A. Z., M. Boaventura, and E. C. Silva, 2005 Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters. Computational & Applied Mathematics 24: 131–150.
  • Brezis, H., 1987 Analyse Fonctionnelle: Theorie et Applications. Masson, Paris, 1987 (2e Tirage).
  • Catté, F., P. Lions, J. Morel, and T. Coll, 1992 Image selective smoothing and edge detection by nonlinear diffusion*. SIAM J. Numer. Anal. 29: 182–193.
  • Chan, T. F., G. H. Golub, and P. Mulet, 1999 A nonlinear primaldual method for total variation-based image restoration. SIAM J. Sci. Comput. 20: 1964–1977.
  • Chang, Q. and I.-L. Chern, 2003 Acceleration methods for total variation-based image denoising. SIAM Journal on Scientific Computing 25: 982–994.
  • Charbonnier, P., L. Blanc-Féraud, G. Aubert, and M. Barlaud, 1994 Two deterministic half-quadratic regularization algorithms for computed imaging. Proceedings of 1st International Conference on Image Processing 2: 168–172 vol.2.
  • Chen, Y.-G., Y. Giga, and S. Goto, 1999 pp. 375–412 in Uniqueness and Existence of Viscosity Solutions of Generalized mean Curvature Flow Equations, edited by Ball, J. M., D. Kinderlehrer, P. Podio- Guidugli, and M. Slemrod, Springer Berlin Heidelberg.
  • El-Fallah, A. I. and G. E. Ford, 1998 On mean curvature diffusion in nonlinear image filtering. Pattern Recognition Letters 19: 433– 437.
  • El-Shorbagy, M. A., M. u. Rahman, and Y. Karaca, 2023 A computational analysis fractional complex-order values by abc operator and mittag-leffler kernel modeling. Fractals 0: null.
  • Gilboa, G., N. Sochen, and Y. Zeevi, 2006 Variational denoising of partly textured images by spatially varying constraints. IEEE Transactions on Image Processing 15: 2281–2289.
  • Haidong, Q., M. ur Rahman, S. E. Al Hazmi, M. F. Yassen, S. Salahshour, et al., 2023 Analysis of non-equilibrium 4d dynamical system with fractal fractional mittag-leffler kernel. Engineering Science and Technology, an International Journal 37: 101319.
  • Kumar, S. and K. Alam, 2021a A new class of nonlinear hyperbolicparabolic model for image denoising with forward-backward diffusivity. Mathematics in Engineering, Science & Aerospace 12: 435–441.
  • Kumar, S. and K. Alam, 2021b Pde-based hyperbolic-parabolic model for image denoising with forward-backward diffusivity. Computational Methods for Differential Equations 9: 1100–1108.
  • Lapidus, L. and G. F. Pinder, 1983 Numerical solution of partial differential equations in science and engineering. SIAM Review 25: 581–582.
  • Li, M.-M. and B.-Z. Li, 2021 A novel weighted total variation model for image denoising. IET Image Processing 15: 2749–2760.
  • Marquina, A. and S. Osher, 2000 Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal. SIAM Journal on Scientific Computing 22: 387–405.
  • Phan, T. D. K., 2020 A weighted total variation based image denoising model using mean curvature. Optik 217: 164940.
  • Prasath, V. B. S. and D. Vorotnikov, 2014 Weighted and wellbalanced anisotropic diffusion scheme for image denoising and restoration. Nonlinear Analysis-real World Applications 17: 33– 46.
  • Qu, H.-D., X. Liu, X. Lu, M. ur Rahman, and Z.-H. She, 2022 Neural network method for solving nonlinear fractional advectiondiffusion equation with spatiotemporal variable-order. Chaos, Solitons & Fractals 156: 111856.
  • Rudin, L. I., S. Osher, and E. Fatemi, 1992 Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60: 259–268.
  • Smolka, B., 2008 Modified biased anisotropic diffusion processing of noisy color images. In 2008 9th International Conference on Signal Processing, pp. 777–780.
  • Vogel, C. R. and M. E. Oman, 1996 Iterative methods for total variation denoising. SIAM Journal on Scientific Computing 17: 227–238.
  • Weickert, J., 1997 A review of nonlinear diffusion filtering. In Scale- Space Theory in Computer Vision, edited by B. ter Haar Romeny, L. Florack, J. Koenderink, and M. Viergever, pp. 1–28, Berlin, Heidelberg, Springer Berlin Heidelberg.
  • XU, C., M. UR RAHMAN, B. FATIMA, and Y. KARACA, 2022 Theoretical and numerical investigation of complexities in fractional-order chaotic system having torus attractors. Fractals 30: 2250164.

Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising

Yıl 2023, Cilt: 5 Sayı: 4, 300 - 307, 31.12.2023
https://doi.org/10.51537/chaos.1324355

Öz

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.

Kaynakça

  • Álvarez, L., P.-L. Lions, and J.-M. Morel, 1992 Image selective smoothing and edge detection by nonlinear diffusion. ii. SIAM Journal on Numerical Analysis 29: 845–866.
  • Barcelos, C., M. Boaventura, and E. Silva, 2003 A well-balanced flow equation for noise removal and edge detection. IEEE Transactions on Image Processing 12: 751–763.
  • Barcelos, C. A. Z., M. Boaventura, and E. C. Silva, 2005 Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters. Computational & Applied Mathematics 24: 131–150.
  • Brezis, H., 1987 Analyse Fonctionnelle: Theorie et Applications. Masson, Paris, 1987 (2e Tirage).
  • Catté, F., P. Lions, J. Morel, and T. Coll, 1992 Image selective smoothing and edge detection by nonlinear diffusion*. SIAM J. Numer. Anal. 29: 182–193.
  • Chan, T. F., G. H. Golub, and P. Mulet, 1999 A nonlinear primaldual method for total variation-based image restoration. SIAM J. Sci. Comput. 20: 1964–1977.
  • Chang, Q. and I.-L. Chern, 2003 Acceleration methods for total variation-based image denoising. SIAM Journal on Scientific Computing 25: 982–994.
  • Charbonnier, P., L. Blanc-Féraud, G. Aubert, and M. Barlaud, 1994 Two deterministic half-quadratic regularization algorithms for computed imaging. Proceedings of 1st International Conference on Image Processing 2: 168–172 vol.2.
  • Chen, Y.-G., Y. Giga, and S. Goto, 1999 pp. 375–412 in Uniqueness and Existence of Viscosity Solutions of Generalized mean Curvature Flow Equations, edited by Ball, J. M., D. Kinderlehrer, P. Podio- Guidugli, and M. Slemrod, Springer Berlin Heidelberg.
  • El-Fallah, A. I. and G. E. Ford, 1998 On mean curvature diffusion in nonlinear image filtering. Pattern Recognition Letters 19: 433– 437.
  • El-Shorbagy, M. A., M. u. Rahman, and Y. Karaca, 2023 A computational analysis fractional complex-order values by abc operator and mittag-leffler kernel modeling. Fractals 0: null.
  • Gilboa, G., N. Sochen, and Y. Zeevi, 2006 Variational denoising of partly textured images by spatially varying constraints. IEEE Transactions on Image Processing 15: 2281–2289.
  • Haidong, Q., M. ur Rahman, S. E. Al Hazmi, M. F. Yassen, S. Salahshour, et al., 2023 Analysis of non-equilibrium 4d dynamical system with fractal fractional mittag-leffler kernel. Engineering Science and Technology, an International Journal 37: 101319.
  • Kumar, S. and K. Alam, 2021a A new class of nonlinear hyperbolicparabolic model for image denoising with forward-backward diffusivity. Mathematics in Engineering, Science & Aerospace 12: 435–441.
  • Kumar, S. and K. Alam, 2021b Pde-based hyperbolic-parabolic model for image denoising with forward-backward diffusivity. Computational Methods for Differential Equations 9: 1100–1108.
  • Lapidus, L. and G. F. Pinder, 1983 Numerical solution of partial differential equations in science and engineering. SIAM Review 25: 581–582.
  • Li, M.-M. and B.-Z. Li, 2021 A novel weighted total variation model for image denoising. IET Image Processing 15: 2749–2760.
  • Marquina, A. and S. Osher, 2000 Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal. SIAM Journal on Scientific Computing 22: 387–405.
  • Phan, T. D. K., 2020 A weighted total variation based image denoising model using mean curvature. Optik 217: 164940.
  • Prasath, V. B. S. and D. Vorotnikov, 2014 Weighted and wellbalanced anisotropic diffusion scheme for image denoising and restoration. Nonlinear Analysis-real World Applications 17: 33– 46.
  • Qu, H.-D., X. Liu, X. Lu, M. ur Rahman, and Z.-H. She, 2022 Neural network method for solving nonlinear fractional advectiondiffusion equation with spatiotemporal variable-order. Chaos, Solitons & Fractals 156: 111856.
  • Rudin, L. I., S. Osher, and E. Fatemi, 1992 Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60: 259–268.
  • Smolka, B., 2008 Modified biased anisotropic diffusion processing of noisy color images. In 2008 9th International Conference on Signal Processing, pp. 777–780.
  • Vogel, C. R. and M. E. Oman, 1996 Iterative methods for total variation denoising. SIAM Journal on Scientific Computing 17: 227–238.
  • Weickert, J., 1997 A review of nonlinear diffusion filtering. In Scale- Space Theory in Computer Vision, edited by B. ter Haar Romeny, L. Florack, J. Koenderink, and M. Viergever, pp. 1–28, Berlin, Heidelberg, Springer Berlin Heidelberg.
  • XU, C., M. UR RAHMAN, B. FATIMA, and Y. KARACA, 2022 Theoretical and numerical investigation of complexities in fractional-order chaotic system having torus attractors. Fractals 30: 2250164.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Elektrik Mühendisliği (Diğer)
Bölüm Research Articles
Yazarlar

Alka Chauhan 0009-0002-2957-4916

Santosh Kumar 0000-0001-9500-7229

Khursheed Alam 0000-0003-4168-3736

Yayımlanma Tarihi 31 Aralık 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 5 Sayı: 4

Kaynak Göster

APA Chauhan, A., Kumar, S., & Alam, K. (2023). Weighted and Well-Balanced Nonlinear TV-Based Time-Dependent Model for Image Denoising. Chaos Theory and Applications, 5(4), 300-307. https://doi.org/10.51537/chaos.1324355

Chaos Theory and Applications in Applied Sciences and Engineering: An interdisciplinary journal of nonlinear science 23830 28903   

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