Skip to main content

2017 | OriginalPaper | Buchkapitel

A Unified Framework for the Restoration of Images Corrupted by Additive White Noise

verfasst von : Alessandro Lanza, Federica Sciacchitano, Serena Morigi, Fiorella Sgallari

Erschienen in: Scale Space and Variational Methods in Computer Vision

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We propose a robust variational model for the restoration of images corrupted by blur and the general class of additive white noises. The solution of the non-trivial optimization problem, due to the non-smooth non-convex proposed model, is efficiently obtained by an Alternating Directions Method of Multipliers (ADMM), which in particular reduces the solution to a sequence of convex optimization sub-problems. Numerical results show the potentiality of the proposed model for restoring blurred images corrupted by several kinds of additive white noises.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
2.
Zurück zum Zitat Bouman, C., Sauer, K.: A generalized Gaussian image model for edge-preserving MAP estimation. IEEE Trans. Image Process. 2(3), 296–310 (1993)CrossRef Bouman, C., Sauer, K.: A generalized Gaussian image model for edge-preserving MAP estimation. IEEE Trans. Image Process. 2(3), 296–310 (1993)CrossRef
3.
Zurück zum Zitat Bovik, A.C.: Handbook of Image and Video Processing. Academic Press, Cambridge (2010)MATH Bovik, A.C.: Handbook of Image and Video Processing. Academic Press, Cambridge (2010)MATH
4.
Zurück zum Zitat Lanza, A., Morigi, S., Sgallari, F., Wen, Y.W.: Image restoration with Poisson-Gaussian mixed noise. Comput. Methods Biomech. Biomed. Eng.: Imaging Vis. 2(1), 12–24 (2013) Lanza, A., Morigi, S., Sgallari, F., Wen, Y.W.: Image restoration with Poisson-Gaussian mixed noise. Comput. Methods Biomech. Biomed. Eng.: Imaging Vis. 2(1), 12–24 (2013)
6.
Zurück zum Zitat Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Model. Simul. 7(3), 1005–1028 (2009)MathSciNetCrossRefMATH Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Model. Simul. 7(3), 1005–1028 (2009)MathSciNetCrossRefMATH
7.
Zurück zum Zitat Keren, D., Werman, M.: Probabilistic analysis of regularization. IEEE Trans. Pattern Anal. Mach. Intell. 15(10), 982–995 (1993)CrossRef Keren, D., Werman, M.: Probabilistic analysis of regularization. IEEE Trans. Pattern Anal. Mach. Intell. 15(10), 982–995 (1993)CrossRef
8.
Zurück zum Zitat Lanza, A., Morigi, S., Sgallari, F., Yezzi, A.J.: Variational image denoising based on autocorrelation whiteness. SIAM J. Imaging Sci. 6(4), 1931–1955 (2013)MathSciNetCrossRefMATH Lanza, A., Morigi, S., Sgallari, F., Yezzi, A.J.: Variational image denoising based on autocorrelation whiteness. SIAM J. Imaging Sci. 6(4), 1931–1955 (2013)MathSciNetCrossRefMATH
9.
Zurück zum Zitat Lanza, A., Morigi, S., Sgallari, F.: Variational image restoration with constraints on noise whiteness. J. Math. Imaging Vis. 53(1), 61–77 (2015)MathSciNetCrossRefMATH Lanza, A., Morigi, S., Sgallari, F.: Variational image restoration with constraints on noise whiteness. J. Math. Imaging Vis. 53(1), 61–77 (2015)MathSciNetCrossRefMATH
10.
Zurück zum Zitat Chan, R.H., Lanza, A., Morigi, S., Sgallari, F.: An adaptive strategy for the restoration of textured images using fractional order regularization. Numer. Math.: Theory Methods Appl. 6(1), 276–296 (2013)MathSciNetMATH Chan, R.H., Lanza, A., Morigi, S., Sgallari, F.: An adaptive strategy for the restoration of textured images using fractional order regularization. Numer. Math.: Theory Methods Appl. 6(1), 276–296 (2013)MathSciNetMATH
11.
Zurück zum Zitat Nikolova, M.: A variational approach to remove outliers and impulse noise. J. Math. Imaging Vis. 20(1), 99–120 (2004)MathSciNetCrossRef Nikolova, M.: A variational approach to remove outliers and impulse noise. J. Math. Imaging Vis. 20(1), 99–120 (2004)MathSciNetCrossRef
12.
Zurück zum Zitat Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60(1–4), 259–268 (1992)MathSciNetCrossRefMATH Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60(1–4), 259–268 (1992)MathSciNetCrossRefMATH
13.
Zurück zum Zitat Sciacchitano, F., Dong, Y., Zeng, T.: Variational approach for restoring blurred images with cauchy noise. SIAM J. Imaging Sc. 8(3), 1894–1922 (2015)MathSciNetCrossRefMATH Sciacchitano, F., Dong, Y., Zeng, T.: Variational approach for restoring blurred images with cauchy noise. SIAM J. Imaging Sc. 8(3), 1894–1922 (2015)MathSciNetCrossRefMATH
14.
Zurück zum Zitat Widrow, B., Kollár, I.: Quantization Noise: Roundoff Error in Digital Computation, Signal Processing, Control, and Communications. Cambridge University Press, New York (2008)CrossRef Widrow, B., Kollár, I.: Quantization Noise: Roundoff Error in Digital Computation, Signal Processing, Control, and Communications. Cambridge University Press, New York (2008)CrossRef
15.
Zurück zum Zitat Lanza, A., Morigi, S., Sgallari, F.: Constrained TV\(_p\)-\(\ell _2\) model for image restoration. J. Sci. Comput. 68(1), 64–91 (2016)MathSciNetCrossRefMATH Lanza, A., Morigi, S., Sgallari, F.: Constrained TV\(_p\)-\(\ell _2\) model for image restoration. J. Sci. Comput. 68(1), 64–91 (2016)MathSciNetCrossRefMATH
16.
Zurück zum Zitat Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)CrossRefMATH Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3(1), 1–122 (2011)CrossRefMATH
17.
Zurück zum Zitat Wu, C., Zhang, J., Tai, X.C.: Augmented lagrangian method for total variation restoration with non-quadratic fidelity. Inverse Probl. Imaging 5(1), 237–261 (2011)MathSciNetCrossRefMATH Wu, C., Zhang, J., Tai, X.C.: Augmented lagrangian method for total variation restoration with non-quadratic fidelity. Inverse Probl. Imaging 5(1), 237–261 (2011)MathSciNetCrossRefMATH
Metadaten
Titel
A Unified Framework for the Restoration of Images Corrupted by Additive White Noise
verfasst von
Alessandro Lanza
Federica Sciacchitano
Serena Morigi
Fiorella Sgallari
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-58771-4_40