Abstract
To separate oscillating parts such as texture and noise from piecewise smooth parts, a new variational image decomposition model is presented, which well improve the novel Starck’s model. The second generation curvelets and wave atoms are used to represent structure and texture respectively. The total variation semi-norm is added for restricting structure parts. The generalized homogeneous Besov norm proposed by Meyer is used to constrain noisy components. Finally, the Basis Pursuit Denoisiing algorithm is used to solve the new model. Experiments show that the approach is very robust to noise, and that can keep edges and textures stably.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Meyer, Y.: Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. American Mathematical Society, Providence (2001)
Chen, S., Donoho, D., Saunder, M.: Atomic Decomposition by Basis Pursuit. SIAM Journal on Scientific Computing 20(1), 33–61 (1998)
Starck, J.L., Candes, E., Donoho, D.: Astronomical Image Representation by the Curvelet transform. Astronomy and Astrophysics 398(2), 785–800 (2003)
Aujol, J.F., Chambolle, A.: Dual Norms and Image Decomposition Models. International Journal of Computer Vision 63(1), 85–104 (2005)
Starck, J.L., Elad, M., Donoho, D.L.: Image Decomposition: Separation of Texture from Piecewise Smooth Content. In: Proceedings of SPIE, San Diego, California, USA, vol. 5207, pp. 571–582 (2003)
Aujol, J.F., Aubert, G., Blanc-Féraud, L., et al.: Image Decomposition Into a Bounded Variation Component and an Oscillating Component. Journal of Mathematical Imaging and Vision 22(1), 71–88 (2005)
Vese, L., Osher, S.: Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing. Journal of Scientific Computing 19(1), 553–572 (2003)
Bai, J., Feng, X.: Image Decomposition by Curvelet Transform. Acta Electronics China 35(1), 123–126 (2007)
Osher, S., Sole, A., Vese, L.: Image Decomposition and Restoration Using Total Variation Minimization and the H-1 Norm. Journal of Multiscale Modeling and Simulation 1(3), 349–370 (2003)
Candes, E.J., Donoho, D.L.: Curvelets: a Surprisingly Effective Nonadaptive Representation for Objects with Edges, pp. 1–16. Department of Statistics, Stanford University, Stanford (1999)
Candes, E.J., Donoho, D.L.: New Tight Frames of Curvelets and Optimal Representations of Objects with Piecewise C2 Singularities. In: Applied and Computational Mathematics, California Institute of Technology, Pasadena, California, USA, pp. 1–68 (2002)
Candes, E.J., Demanet, L., Donoho, D.L.: Fast Discrete Curvelet Transforms. In: Applied and Computational Mathematics, California Institute of Technology, Pasadena, California, USA, pp. 1–43 (2005)
Demanet, L., Ying, L.X.: Wave Atoms and Sparsity of Oscillatory Patterns. Appl. Comput. Harmon. Anal. 23(3), 368–387 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lu, C. (2008). Image Decomposition Based on Curvelet and Wave Atom. In: Kang, L., Cai, Z., Yan, X., Liu, Y. (eds) Advances in Computation and Intelligence. ISICA 2008. Lecture Notes in Computer Science, vol 5370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92137-0_75
Download citation
DOI: https://doi.org/10.1007/978-3-540-92137-0_75
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92136-3
Online ISBN: 978-3-540-92137-0
eBook Packages: Computer ScienceComputer Science (R0)