Applications of sampling Kantorovich operators to thermographic images for seismic engineering

Journal of Computational Analysis and Applications

Volumn 19, Issue 1, 2015, Pages 1-16

  Cluni, Federico ^a   Costarelli, Danilo ^b   Minotti, Anna Maria ^a   Vinti, Gianluca ^a  

^a UNIVERSITY OF PERUGIA   (Italy)

^b ROMA TRE UNIVERSITY   (Italy)

Author keywords

Image Processing; Orlicz spaces; Sampling Kantorovich operators; Structural analysis; Thermographic images

Indexed keywords

EID: 84923851309     PISSN: 15211398     EISSN: 15729206     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. L. Angeloni and G. Vinti, Rate of approximation for nonlinear integral operators with applications to signal processing, Differential and Integral Equations, 18 (8), 855-890, 2005.
2. C. Bardaro, P.L. Butzer, R.L. Stens and G. Vinti, Approximation of the Whittaker Sampling Series in terms of an Average Modulus of Smoothness covering Discontinuous Signals, J. Math. Anal. Appl., 316, 269-306, 2006.
3. C. Bardaro, P.L. Butzer, R.L. Stens and G. Vinti, Kantorovich-Type Generalized Sampling Series in the Setting of Orlicz Spaces, Sampling Theory in Signal and Image Processing, 6 (1), 29-52, 2007.
4. C. Bardaro, P.L. Butzer, R.L. Stens and G. Vinti, Prediction by samples from the past with error estimates covering discontinuous signals, IEEE, Transaction on Information Theory, 56 (1), 614-633, 2010.
5. C. Bardaro and I. Mantellini, Modular Approximation by Sequences of Nonlinear Integral Operators in Musielak-Orlicz Spaces, Atti Sem. Mat. Fis. Univ. Modena, special issue dedicated to Professor Calogero Vinti, 46, 403-425, 1998.
6. C. Bardaro and I. Mantellini, On convergence properties for a class of Kantorovich discrete operators, Numer. Funct. Anal. Optim.. 33 (4), 374-396, 2012.
7. C. Bardaro, J. Musielak and G. Vinti, Nonlinear Integral Operators and Applications, De Gruyter Series in Nonlinear Analysis and Applications, New York, Berlin, 9, 2003.
8. C. Bardaro and G. Vinti, Some Inclusion Theorems for Orlicz and Musielak-Orlicz Type Spaces, Annali di Matematica Pura e Applicata, 168, 189-203, 1995.
9. C. Bardaro and G. Vinti, A general approach to the convergence theorems of generalized sampling series, Applicable Analysis, 64, 203-217, 1997.
10. P.L. Butzer, A. Fisher and R.L. Stens, Generalized sampling approximation of multivariate signals: theory and applications, Note di Matematica, 10 (1), 173-191, 1990.
11. P.L. Butzer and R.J. Nessel, Fourier Analysis and Approximation, I, Academic Press, New York-London, 1971.
12. P.L. Butzer and R.L. Stens, Linear prediction by samples from the past, Advanced Topics in Shannon Sampling and Interpolation Theory, (editor R.J. Marks II), Springer-Verlag, New York, 1993.
13. N. Cavalagli, F. Cluni and V. Gusella, Evaluation of a Statistically Equivalent Periodic Unit Cell for a quasi-periodic masonry, International Journal of Solids and Structures, 50, 4226-4240, 2013.
14. F. Cluni and V. Gusella, Homogenization of non-periodic masonry structures, International Journal of Solids and Structures, 41, 1911-1923, 2004.
15. D. Costarelli and G. Vinti, Approximation by Multivariate Generalized Sampling Kantorovich Operators in the Setting of Orlicz Spaces, Bollettino U.M.I., Special volume dedicated to Prof. Giovanni Prodi, 9 (4), 445-468, 2011.
16. D. Costarelli and G. Vinti, Approximation by Nonlinear Multivariate Sampling Kantorovich Type Operators and Applications to Image Processing, Numerical Functional Analysis and Optimization, 34 (8), 819-844, 2013.
17. R. Gonzales and R. Woods, Digital Image Processing, Prentice-Hall NJ - USA, 2002.
18. J. Musielak, Orlicz Spaces and Modular Spaces, Springer-Verlag, Lecture Notes in Math. 1034, 1983.
19. J. Musielak and W. Orlicz, On modular spaces, Studia Math., 28, 49-65, 1959.
20. M.M. Rao and Z.D. Ren, Theory of Orlicz Spaces, Pure and Appl. Math., Marcel Dekker Inc. New York-Basel-Hong Kong, 1991.
21. G. Vinti, A general approximation result for nonlinear integral operators and applications to signal processing, Applicable Analysis, 79, 217-238, 2001.
22. G. Vinti and L. Zampogni, Approximation by means of nonlinear Kantorovich sampling type operators in Orlicz spaces, J. Approx. Theory, 161, 511-528, 2009.
23. G. Vinti and L. Zampogni, A Unifying Approach to Convergence of Linear Sampling Type Operators in Orlicz Spaces, Advances in Differential Equations, 16 (5-6), 573-600, 2011.
24. G. Vinti and L. Zampogni, A Unifying Approach to Convergence of Linear Sampling Type Operators in Orlicz Spaces, Advances in Differential Equations, 16 (5-6), 573-600, 2011.
25. G. Vinti, L. Zampogni, Approximation results for a general class of Kantorovich type operators, in print in Advanced Nonlinear Studies (2014).