-
Previous Article
New methods for local solvability of quasilinear symmetric hyperbolic systems
- EECT Home
- This Issue
-
Next Article
Exponential stability of a coupled system with Wentzell conditions
On a parabolic-hyperbolic filter for multicolor image noise reduction
1. | Taras Shevchenko National University of Kyiv, Faculty of Cybernetics, 4D Glushkov Ave, 03680 Kyiv, Ukraine |
2. | Karlsruhe Institute of Technology, Department of Mathematics, Englerstrasse 2, 76131 Karlsruhe, Germany |
References:
[1] |
L. Alvarez, F. Guichard, P.-L. Lions and J.-M. Morel, Axioms and fundamental equations of image processing,, Archive for Rational Mechanics and Analysis, 123 (1993), 199.
doi: 10.1007/BF00375127. |
[2] |
H. Amann, Compact embeddings of vector-valued Sobolev and Besov spaces,, Glasnik Matematički, 35 (2000), 161.
|
[3] |
H. Amann, Non-local quasi-linear parabolic equations,, Russian Mathematical Surveys, 60 (2005), 1021.
doi: 10.1070/RM2005v060n06ABEH004279. |
[4] |
H. Amann, Time-delayed Perona-Malik type problems,, Acta Mathematica Universitatis Comenianae, 76 (2007), 15.
|
[5] |
F. Andreu, C. Ballester, V. Caselles and J. M. Mazón, Minimizing total variational flow,, Differential and Integral Equations, 14 (2001), 321.
|
[6] |
F. Andreu, C. Ballester, V. Caselles and J. M. Mazón, Some qualitative properties for the total variation flow,, Journal of Functional Analysis, 188 (2002), 516.
doi: 10.1006/jfan.2001.3829. |
[7] |
W. Arendt and R. Chill, Global existence for quasilinear diffusion equations in isotropic nondivergence form,, Annali della Scuola Normale Superiore di Pisa (5), 9 (2010), 523.
|
[8] |
V. Barbu, Nonlinear Differential Equations Of Monotone Types in Banach Spaces,, Springer Monographs in Mathematics, (2010).
doi: 10.1007/978-1-4419-5542-5. |
[9] |
A. Belahmidi, Équations Aux Dérivées Partielles Appliquées à la Restauration et à L'agrandissement des Images,, PhD thesis, (2003). Google Scholar |
[10] |
A. Belahmidi and A. Chambolle, Time-delay regularization of anisotropic diffusion and image processing,, ESAIM: Mathematical Modelling and Numerical Analysis, 39 (2005), 231.
doi: 10.1051/m2an:2005010. |
[11] |
A. Belleni-Morante and A. C. McBride, Applied Nonlinear Semigroups: An Introduction,, Wiley Series in Mathematical Methods in Practice, (1998).
|
[12] |
G. Bellettini, V. Caselles and M. Novaga, The total variation flow in $\mathbbR^N$,, Journal of Differential Equations, 184 (2002), 475.
doi: 10.1006/jdeq.2001.4150. |
[13] |
M. Burger, A. C. G. Menucci, S. Osher and M. Rumpf (eds.), Level Set and PDE Based Reconstruction Methods in Imaging, vol. 2090 of Lecture Notes in Mathematics,, Springer International Publishing, (1992). Google Scholar |
[14] |
J. Canny, Finding Edges and Lines in Images,, Technical Report 720, (1983). Google Scholar |
[15] |
G. R. Cattaneo, Sur une forme de l'équation de la chaleur éliminant le paradoxe d'une propagation instantanée,, Comptes Rendus de l'Académie des Sciences, 247 (1958), 431.
|
[16] |
F. Catté, P.-L. Lions, J.-M. Morel and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion,, SIAM Journal on Numerical Analysis, 29 (1992), 182.
doi: 10.1137/0729012. |
[17] |
G. H. Cottet and M. El Ayyadi, A Volterra type model for image processing,, IEEE Transactions on Image Processing, 7 (1998), 292.
doi: 10.1109/83.661179. |
[18] |
R. Dautray and J.-L. Lions, Evolution Problems, vol. 5 of Mathematical Analysis and Numerical Methods for Science and Technology,, Springer-Verlag, (1992).
doi: 10.1007/978-3-642-58090-1. |
[19] |
D. Dier, Non-autonomous maximal regularity for forms of bounded variation,, Journal of Mathematical Analysis and Applications, 425 (2015), 33.
doi: 10.1016/j.jmaa.2014.12.006. |
[20] |
M. E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds,, Archive for Rational Mechanics and Analysis, 31 (1968), 113.
doi: 10.1007/BF00281373. |
[21] |
A. Handlovičová, K. Mikula and F. Sgallari, Variational numerical methods for solving nonlinear diffusion equations arising in image processing,, Journal of Visual Communication and Image Representation, 13 (2002), 217. Google Scholar |
[22] |
M. Hieber and M. Murata, The $L^p$-approach to the fluid-rigid body interaction problem for compressible fluids,, Evolution Equations and Control Theory, 4 (2015), 69.
doi: 10.3934/eect.2015.4.69. |
[23] |
M. Hochbruck, T. Jahnke and R. Schnaubelt, Convergence of an ADI splitting for Maxwell's equations,, Numerische Mathematik, 129 (2015), 535.
doi: 10.1007/s00211-014-0642-0. |
[24] |
S. L. Keeling and R. Stollberger, Nonlinear anisotropic diffusion filtering for multiscale edge enhancement,, Inverse Problems, 18 (2002), 175.
doi: 10.1088/0266-5611/18/1/312. |
[25] |
D. Marr and E. Hildreth, Theory of edge detection,, Proceedings of the Royal Society B, 207 (1980), 187.
doi: 10.1098/rspb.1980.0020. |
[26] |
S. A. Morris, The Schauder-Tychonoff fixed point theorem and applications,, Matematický Časopis, 25 (1975), 165.
|
[27] |
M. Nitzberg and T. Shiota, Nonlinear image filtering with edge and corner enhancement,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 14 (1992), 826.
doi: 10.1109/34.149593. |
[28] |
T. Ohkubo, Regularity of solutions to hyperbolic mixed problems with uniformly characteristic boundary,, Hokkaido Mathematical Journal, 10 (1981), 93.
doi: 10.14492/hokmj/1381758116. |
[29] |
P. Perona and J. Malik, Scale space and edge detection using anisotropic diffusion,, IEEE Trans. Pattern Anal. Machine Intell., 12 (1990), 629.
doi: 10.1109/34.56205. |
[30] |
J. Prüss, Maximal regularity of linear vector-valued parabolic Volterra equations,, Journal of Integral Equations and Applications, 3 (1991), 63.
doi: 10.1216/jiea/1181075601. |
[31] |
J. Prüss, Evolutionary Integral Equations and Applications, vol. 87 of Monographs in Mathematics,, Birkhäuser Verlag, (1993).
doi: 10.1007/978-3-0348-8570-6. |
[32] |
L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms,, Physica D: Nonlinear Phenomena, 60 (1992), 259.
doi: 10.1016/0167-2789(92)90242-F. |
[33] |
G. Savaré, Regularity results for elliptic equations in Lipschitz domains,, Journal of Functional Analysis, 152 (1998), 176.
doi: 10.1006/jfan.1997.3158. |
[34] |
D. W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization,, 2nd edition, ().
|
[35] |
P. Secchi, Well-posedness of characteristic symmetric hyperbolic systems,, Archive for Rational Mechanics and Analysis, 134 (1996), 155.
doi: 10.1007/BF00379552. |
[36] |
K. Takezawa, Introduction to Nonparametric Regression,, Wiley Series in Probability and Mathematical Statistics, (2006).
|
[37] |
J. Weickert, Anisotropic Diffusion in Image Processing,, B. G. Teubner, (1998).
|
[38] |
A. P. Witkin, Scale-space filtering,, Readings in Computer Vision: Issues, (1987), 329.
doi: 10.1016/B978-0-08-051581-6.50036-2. |
[39] |
R. Zacher, Maximal regularity of type $L_p$ for abstract parabolic Volterra equations,, Journal of Evolution Equations, 5 (2005), 79.
doi: 10.1007/s00028-004-0161-z. |
show all references
References:
[1] |
L. Alvarez, F. Guichard, P.-L. Lions and J.-M. Morel, Axioms and fundamental equations of image processing,, Archive for Rational Mechanics and Analysis, 123 (1993), 199.
doi: 10.1007/BF00375127. |
[2] |
H. Amann, Compact embeddings of vector-valued Sobolev and Besov spaces,, Glasnik Matematički, 35 (2000), 161.
|
[3] |
H. Amann, Non-local quasi-linear parabolic equations,, Russian Mathematical Surveys, 60 (2005), 1021.
doi: 10.1070/RM2005v060n06ABEH004279. |
[4] |
H. Amann, Time-delayed Perona-Malik type problems,, Acta Mathematica Universitatis Comenianae, 76 (2007), 15.
|
[5] |
F. Andreu, C. Ballester, V. Caselles and J. M. Mazón, Minimizing total variational flow,, Differential and Integral Equations, 14 (2001), 321.
|
[6] |
F. Andreu, C. Ballester, V. Caselles and J. M. Mazón, Some qualitative properties for the total variation flow,, Journal of Functional Analysis, 188 (2002), 516.
doi: 10.1006/jfan.2001.3829. |
[7] |
W. Arendt and R. Chill, Global existence for quasilinear diffusion equations in isotropic nondivergence form,, Annali della Scuola Normale Superiore di Pisa (5), 9 (2010), 523.
|
[8] |
V. Barbu, Nonlinear Differential Equations Of Monotone Types in Banach Spaces,, Springer Monographs in Mathematics, (2010).
doi: 10.1007/978-1-4419-5542-5. |
[9] |
A. Belahmidi, Équations Aux Dérivées Partielles Appliquées à la Restauration et à L'agrandissement des Images,, PhD thesis, (2003). Google Scholar |
[10] |
A. Belahmidi and A. Chambolle, Time-delay regularization of anisotropic diffusion and image processing,, ESAIM: Mathematical Modelling and Numerical Analysis, 39 (2005), 231.
doi: 10.1051/m2an:2005010. |
[11] |
A. Belleni-Morante and A. C. McBride, Applied Nonlinear Semigroups: An Introduction,, Wiley Series in Mathematical Methods in Practice, (1998).
|
[12] |
G. Bellettini, V. Caselles and M. Novaga, The total variation flow in $\mathbbR^N$,, Journal of Differential Equations, 184 (2002), 475.
doi: 10.1006/jdeq.2001.4150. |
[13] |
M. Burger, A. C. G. Menucci, S. Osher and M. Rumpf (eds.), Level Set and PDE Based Reconstruction Methods in Imaging, vol. 2090 of Lecture Notes in Mathematics,, Springer International Publishing, (1992). Google Scholar |
[14] |
J. Canny, Finding Edges and Lines in Images,, Technical Report 720, (1983). Google Scholar |
[15] |
G. R. Cattaneo, Sur une forme de l'équation de la chaleur éliminant le paradoxe d'une propagation instantanée,, Comptes Rendus de l'Académie des Sciences, 247 (1958), 431.
|
[16] |
F. Catté, P.-L. Lions, J.-M. Morel and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion,, SIAM Journal on Numerical Analysis, 29 (1992), 182.
doi: 10.1137/0729012. |
[17] |
G. H. Cottet and M. El Ayyadi, A Volterra type model for image processing,, IEEE Transactions on Image Processing, 7 (1998), 292.
doi: 10.1109/83.661179. |
[18] |
R. Dautray and J.-L. Lions, Evolution Problems, vol. 5 of Mathematical Analysis and Numerical Methods for Science and Technology,, Springer-Verlag, (1992).
doi: 10.1007/978-3-642-58090-1. |
[19] |
D. Dier, Non-autonomous maximal regularity for forms of bounded variation,, Journal of Mathematical Analysis and Applications, 425 (2015), 33.
doi: 10.1016/j.jmaa.2014.12.006. |
[20] |
M. E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds,, Archive for Rational Mechanics and Analysis, 31 (1968), 113.
doi: 10.1007/BF00281373. |
[21] |
A. Handlovičová, K. Mikula and F. Sgallari, Variational numerical methods for solving nonlinear diffusion equations arising in image processing,, Journal of Visual Communication and Image Representation, 13 (2002), 217. Google Scholar |
[22] |
M. Hieber and M. Murata, The $L^p$-approach to the fluid-rigid body interaction problem for compressible fluids,, Evolution Equations and Control Theory, 4 (2015), 69.
doi: 10.3934/eect.2015.4.69. |
[23] |
M. Hochbruck, T. Jahnke and R. Schnaubelt, Convergence of an ADI splitting for Maxwell's equations,, Numerische Mathematik, 129 (2015), 535.
doi: 10.1007/s00211-014-0642-0. |
[24] |
S. L. Keeling and R. Stollberger, Nonlinear anisotropic diffusion filtering for multiscale edge enhancement,, Inverse Problems, 18 (2002), 175.
doi: 10.1088/0266-5611/18/1/312. |
[25] |
D. Marr and E. Hildreth, Theory of edge detection,, Proceedings of the Royal Society B, 207 (1980), 187.
doi: 10.1098/rspb.1980.0020. |
[26] |
S. A. Morris, The Schauder-Tychonoff fixed point theorem and applications,, Matematický Časopis, 25 (1975), 165.
|
[27] |
M. Nitzberg and T. Shiota, Nonlinear image filtering with edge and corner enhancement,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 14 (1992), 826.
doi: 10.1109/34.149593. |
[28] |
T. Ohkubo, Regularity of solutions to hyperbolic mixed problems with uniformly characteristic boundary,, Hokkaido Mathematical Journal, 10 (1981), 93.
doi: 10.14492/hokmj/1381758116. |
[29] |
P. Perona and J. Malik, Scale space and edge detection using anisotropic diffusion,, IEEE Trans. Pattern Anal. Machine Intell., 12 (1990), 629.
doi: 10.1109/34.56205. |
[30] |
J. Prüss, Maximal regularity of linear vector-valued parabolic Volterra equations,, Journal of Integral Equations and Applications, 3 (1991), 63.
doi: 10.1216/jiea/1181075601. |
[31] |
J. Prüss, Evolutionary Integral Equations and Applications, vol. 87 of Monographs in Mathematics,, Birkhäuser Verlag, (1993).
doi: 10.1007/978-3-0348-8570-6. |
[32] |
L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms,, Physica D: Nonlinear Phenomena, 60 (1992), 259.
doi: 10.1016/0167-2789(92)90242-F. |
[33] |
G. Savaré, Regularity results for elliptic equations in Lipschitz domains,, Journal of Functional Analysis, 152 (1998), 176.
doi: 10.1006/jfan.1997.3158. |
[34] |
D. W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization,, 2nd edition, ().
|
[35] |
P. Secchi, Well-posedness of characteristic symmetric hyperbolic systems,, Archive for Rational Mechanics and Analysis, 134 (1996), 155.
doi: 10.1007/BF00379552. |
[36] |
K. Takezawa, Introduction to Nonparametric Regression,, Wiley Series in Probability and Mathematical Statistics, (2006).
|
[37] |
J. Weickert, Anisotropic Diffusion in Image Processing,, B. G. Teubner, (1998).
|
[38] |
A. P. Witkin, Scale-space filtering,, Readings in Computer Vision: Issues, (1987), 329.
doi: 10.1016/B978-0-08-051581-6.50036-2. |
[39] |
R. Zacher, Maximal regularity of type $L_p$ for abstract parabolic Volterra equations,, Journal of Evolution Equations, 5 (2005), 79.
doi: 10.1007/s00028-004-0161-z. |
[1] |
José Luiz Boldrini, Jonathan Bravo-Olivares, Eduardo Notte-Cuello, Marko A. Rojas-Medar. Asymptotic behavior of weak and strong solutions of the magnetohydrodynamic equations. Electronic Research Archive, 2021, 29 (1) : 1783-1801. doi: 10.3934/era.2020091 |
[2] |
Jens Lorenz, Wilberclay G. Melo, Suelen C. P. de Souza. Regularity criteria for weak solutions of the Magneto-micropolar equations. Electronic Research Archive, 2021, 29 (1) : 1625-1639. doi: 10.3934/era.2020083 |
[3] |
Martin Kalousek, Joshua Kortum, Anja Schlömerkemper. Mathematical analysis of weak and strong solutions to an evolutionary model for magnetoviscoelasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 17-39. doi: 10.3934/dcdss.2020331 |
[4] |
Lorenzo Zambotti. A brief and personal history of stochastic partial differential equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 471-487. doi: 10.3934/dcds.2020264 |
[5] |
Hua Chen, Yawei Wei. Multiple solutions for nonlinear cone degenerate elliptic equations. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020272 |
[6] |
Alex H. Ardila, Mykael Cardoso. Blow-up solutions and strong instability of ground states for the inhomogeneous nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2021, 20 (1) : 101-119. doi: 10.3934/cpaa.2020259 |
[7] |
Rim Bourguiba, Rosana Rodríguez-López. Existence results for fractional differential equations in presence of upper and lower solutions. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1723-1747. doi: 10.3934/dcdsb.2020180 |
[8] |
Yueyang Zheng, Jingtao Shi. A stackelberg game of backward stochastic differential equations with partial information. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020047 |
[9] |
Junyong Eom, Kazuhiro Ishige. Large time behavior of ODE type solutions to nonlinear diffusion equations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3395-3409. doi: 10.3934/dcds.2019229 |
[10] |
Tianwen Luo, Tao Tao, Liqun Zhang. Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3737-3765. doi: 10.3934/dcds.2019230 |
[11] |
Yang Liu. Global existence and exponential decay of strong solutions to the cauchy problem of 3D density-dependent Navier-Stokes equations with vacuum. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1291-1303. doi: 10.3934/dcdsb.2020163 |
[12] |
Serge Dumont, Olivier Goubet, Youcef Mammeri. Decay of solutions to one dimensional nonlinear Schrödinger equations with white noise dispersion. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020456 |
[13] |
Cheng He, Changzheng Qu. Global weak solutions for the two-component Novikov equation. Electronic Research Archive, 2020, 28 (4) : 1545-1562. doi: 10.3934/era.2020081 |
[14] |
Helmut Abels, Johannes Kampmann. Existence of weak solutions for a sharp interface model for phase separation on biological membranes. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 331-351. doi: 10.3934/dcdss.2020325 |
[15] |
Ryuji Kajikiya. Existence of nodal solutions for the sublinear Moore-Nehari differential equation. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1483-1506. doi: 10.3934/dcds.2020326 |
[16] |
Pierre Baras. A generalization of a criterion for the existence of solutions to semilinear elliptic equations. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 465-504. doi: 10.3934/dcdss.2020439 |
[17] |
Bo Chen, Youde Wang. Global weak solutions for Landau-Lifshitz flows and heat flows associated to micromagnetic energy functional. Communications on Pure & Applied Analysis, 2021, 20 (1) : 319-338. doi: 10.3934/cpaa.2020268 |
[18] |
Thierry Cazenave, Ivan Naumkin. Local smooth solutions of the nonlinear Klein-gordon equation. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020448 |
[19] |
Riadh Chteoui, Abdulrahman F. Aljohani, Anouar Ben Mabrouk. Classification and simulation of chaotic behaviour of the solutions of a mixed nonlinear Schrödinger system. Electronic Research Archive, , () : -. doi: 10.3934/era.2021002 |
[20] |
Hua Qiu, Zheng-An Yao. The regularized Boussinesq equations with partial dissipations in dimension two. Electronic Research Archive, 2020, 28 (4) : 1375-1393. doi: 10.3934/era.2020073 |
2019 Impact Factor: 0.953
Tools
Metrics
Other articles
by authors
[Back to Top]