References
- F. Andreu, C. Ballester, V. Caselles, and J.M. Mazón, Minimizing total variation flow, CRAS I-Mathé matique 331 (2000), pp. 867–872.
- F. Andreu-Vaillo, V. Caselles, and J.M. Mazón, Parabolic Quasilinear Equations Minimizing Linear Growth Functionals, Birkhäuser, Basel, 2004.
- G. Aubert and J.-F. Aujol, Modeling very oscillating signals. Application to image processing, Appl. Math. Opt. 51 (2005), pp. 163–182.
- G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing Partial Differential Equations and the Calculus of Variations, Springer-Verlag, New York, 2003.
- J.-F. Aujol and A Chambolle, Dual norms and image decomposition models, Int. J. Comput. Vision 63 (2003), pp. 85–104.
- J.-F. Aujol, G. Aubert, L. Blanc-Feraud, and A. Chambolle, Image Decomposition Application to SAR Images, Scale Space Methods in Computer Vision, Springer, Berlin, Heidelberg, 2695 (2003), pp. 297–312.
- J.-F. Aujol, G. Aubert, L. Blanc-Feraud, and A. Chambolle, Image decomposition into a bounded variation component and an oscillating component, J. Math. Imaging Vis. 22 (2005), pp. 71–88.
- A. Buades, T.M. Le, J.M. Morel, and L.A. Vese, Fast cartoon + texture image filters, IEEE Trans. Image Process. 19 (2010), pp. 1978–1986.
- F. Cattè, P.L. Lions, J.M. Morel, and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal. 129 (1992), pp. 182–193.
- C.M. Elliott and S.A. McBeth, Analysis of the TV regularization and H−1 fidelity model for decomposing an image into cartoon plus texture, Commun. Pur. Appl. Anal. 6 (2007), pp. 917–936.
- L.C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, American Mathematical Society, Providence, Rhode Island, 1998.
- L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992.
- J. Garnett, T. Le, Y. Meyer, and L. Vese, Image decompositions using bounded variation and generalized homogeneous Besov spaces, Appl. Comput. Harmon. Anal. 23 (2007), pp. 25–56.
- J. Gilles and Y. Meyer, Properties of BV-G structures+textures decomposition models application to road detection in satellite images, IEEE Trans. Image Process. 9 (2010), pp. 2793–2800.
- Z.C. Guo, J.X. Yin, and Q. Liu, On a reaction-Diffusion system applied to image decomposition and restoration, Math. Comput. Model. 53 (2011), pp. 1336–1350.
- Z.C. Guo, Q. Liu, J.B. Sun, and B.Y. Wu, Reaction–diffusion systems with p(x)-growth for image denoising, Nonlinear Anal. Real. 12 (2011), pp. 2904–2918.
- R. Jiwari and J. Yuan, A computational modeling of two dimensional reaction–diffusion Brusselator system arising in chemical processes, J. Math. Chem. 52 (2014), pp. 1535–1551.
- R. Jiwari, S. Tomasiello, F. Tornabene, and C. Li, A numerical algorithm for computational modelling of coupled advection–diffusion–reaction systems, Eng. Comput. 35(3) (2018), pp. 1383–1401.
- S. Kumar, R. Jiwari, and R.C. Mitta, Numerical simulation for computational modelling of reaction–diffusion Brusselator model arising in chemical processes, J. Math. Chem. 57 (2019), pp. 149–179.
- O.A. Ladyzhenskaja, V.A. Solonnikov, and N.N. Ural'tzeva, Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, American Mathematical Society, Providence, Rhode Island, Vol. 23, 1968.
- T. Le and L. Vese, Image decomposition using total variation and div (BMO), Multiscale Model. Sim. 4 (2005), pp. 390–423.
- L. Linh and L. Vese, Image restoration and decomposition via bounded total variation and negative Hilbert–Sobolev spaces, Appl. Math. Opt. 58 (2008), pp. 167–193.
- Q. Liu, Z.A. Yao, and Y.Y. Ke, Entropy solutions for a fourth-order nonlinear degenerate problem for noise removal, Nonlinear Anal. Theor. 67 (2007), pp. 1908–1918.
- J.E. Macías-Díaz, On a boundedness-preserving semi-linear discretization of a two-dimensional nonlinear diffusion–reaction model, Int. J. Comput. Math. 89 (2012), pp. 1678–1688.
- J.E. Macías-Díaz and A.E. González, A convergent and dynamically consistent finite-difference method to approximate the positive and bounded solutions of the classical Burgers–Fisher equation, J. Comput. Appl. Math. 318 (2017), pp. 604–615.
- J.E. Macías-Díaz and A. Szafrańska, Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation, J. Differ. Equ. Appl. 20 (2014), pp. 989–1004.
- Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, University Lecture Series, American Mathematical Society, Providence, Rhode Island, Vol. 22, 2002.
- R.C. Mittal, S. Kumar, and R. Jiwari, A cubic B-spline quasi-interpolation algorithm to capture the pattern formation of coupled reaction–diffusion models, Eng. Comput. (2021). doi:https://doi.org/10.1007/s00366-020-01278-3
- S. Osher, A. Solé, and L. Vese, Image decomposition and restoration using total variation minimization and the H−1 norm, Multiscale Model. Sim. 3 (2003), pp. 349–370.
- P. Perona and Malik, Scale space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell. 12 (1990), pp. 629–639.
- L. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D 60 (1992), pp. 259–268.
- A. Szafrańska and J.E. Macías-Díaz, On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers-Huxley equation, J. Differ. Equ. Appl. 20 (2014), pp. 1444–1451.
- L. Vese and S. Osher, Modeling textures with total variation minimization and oscillating patterns in image processing, J. Sci. Comput. 19 (2003), pp. 553–572.
- Z.Q. Wu, Q.N. Zhao, J.X. Yin, and H.L. Li, Nonlinear Diffusion Equations, World Scientific, Singapore, 2001.
- Z.Q. Wu, J.X. Yin, and C.P. Wang, Elliptic & Parabolic Equations, World Scientific, Singapore, 2006.
- Y.L. You, W. Xu, A. Tannenbaum, and M. Kaveh, Behavioral analysis of anisotropic diffusion in image processing, IEEE Trans. Image Process. 5 (1996), pp. 1539–1553.