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2011 | 21 | 4 | 769-777
Tytuł artykułu

A well-posed multiscale regularization scheme for digital image denoising

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We propose an edge adaptive digital image denoising and restoration scheme based on space dependent regularization. Traditional gradient based schemes use an edge map computed from gradients alone to drive the regularization. This may lead to the oversmoothing of the input image, and noise along edges can be amplified. To avoid these drawbacks, we make use of a multiscale descriptor given by a contextual edge detector obtained from local variances. Using a smooth transition from the computed edges, the proposed scheme removes noise in flat regions and preserves edges without oscillations. By incorporating a space dependent adaptive regularization parameter, image smoothing is driven along probable edges and not across them. The well-posedness of the corresponding minimization problem is proved in the space of functions of bounded variation. The corresponding gradient descent scheme is implemented and further numerical results illustrate the advantages of using the adaptive parameter in the regularization scheme. Compared with similar edge preserving regularization schemes, the proposed adaptive weight based scheme provides a better multiscale edge map, which in turn produces better restoration.
Rocznik
Tom
21
Numer
4
Strony
769-777
Opis fizyczny
Daty
wydano
2011
otrzymano
2010-11-04
poprawiono
2011-05-19
poprawiono
2011-06-12
Twórcy
  • Department of Mathematics, University of Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal
Bibliografia
  • Aubert, G. and Kornprobst, P. (2006). Mathematical Problems in Image Processing: Partial Differential Equation and Calculus of Variations, Springer-Verlag, New York, NY.
  • Basu, M. (2002). Gaussian based edge-detection methods-A survey, IEEE Transactions on System, Man, and Cybernetics, Part C: Applications and Reviews 32(3): 252-260.
  • Brezis, H. (1973). Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, North-Holland Publishing Company, Amsterdam.
  • Charbonnier, P., Blanc-Feraud, L., Aubert, G. and Barlaud, M. (1997). Deterministic edge-preserving regularization in computed imaging, IEEE Transactions on Image Processing 6(2): 298-311.
  • Chen, Y. and Wunderli, T. (2002). Adaptive total variation for image restoration in BV space, Journal of Mathematical Analysis and Applications 272(3): 117-137.
  • Douiri, A., Schweiger, M., Riley, J. and Arridge, S.R. (2007). Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information, Measurement Science and Technology 18(1): 87-95.
  • Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence 6(6): 721-741.
  • Gilboa, G. and Osher, S. (2007). Nonlocal linear image regaulrization and supervised segmentation, SIAM Journal on Multiscale Modelling and Simulation 6(2): 595-630.
  • Giusti, F. (1984). Minimal Surfaces and Functions of Bounded Variation, Birkhauser, Basel.
  • Lukac, R. and Smolka, B. (2003). Application of the adaptive center-weighted vector median framework for the enhancement of cDNA microarray images, International Journal of Applied Mathematics and Computer Science 13(3): 369-383.
  • Perona, P. and Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence 12(7): 629-639.
  • Prasath, V.B.S. and Singh, A. (2010a). A hybrid convex variational model for image restoration, Applied Mathematics and Computation 215(10): 3655-3664.
  • Prasath, V.B.S. and Singh, A. (2010b). Well-posed inhomogeneous nonlinear diffusion scheme for digital image denoising, Journal of Applied Mathematics, Article ID 763847.
  • Rudin, L., Osher, S. and Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms, Physica D 60 (1-4): 259-268.
  • Santitissadeekorn, N. and Bollt, E.M. (1996). Image edge respecting denoising with edge denoising by a designer nonisotropic structure tensor method, Computational Methods in Applied Mathematics 9(3): 309-318.
  • Strong, D.M. and Chan, T.F. (1996). Spatially and scale adaptive total variation based regularization and anisotropic diffusion in image processing, Technical Report 96-46, Computational and Applied Mathematics, University of California Los Angeles, CA, ftp://ftp.math.ucla.edu/pub/camreport/cam96-46.ps.gz.
  • You, Y.-L. and Kaveh, M. (1999). Blind image restoration by anisotropic regularization, IEEE Transactions on Image Processing 8(3): 396-407.
  • Szeliski, R., Zabih, R., Scharstein, D., Veksler, O., Kolmogorov, V., Agarwala, A., Tapen, M. and Rother, C. (2008). A comparative study of energy minimization methods for Markov random fields with smoothness based priors, IEEE Transactions on Pattern Analysis and Machine Intelligence 30(6): 1068-1080.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv21i4p769bwm
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