Abstract
This paper presents a de-noising method that recognizes similarities in the image through the time scale behaviour of wavelet coefficients. Wavelet details are represented as linear combination of predefined atoms whose center of mass traces trajectories in the time scale plane (from fine to coarse scale). These trajectories are the solution of a proper ordinary differential equation and characterize atoms corresponding to groups of not isolated singularities in the signal. The distances among atoms, the ratio of their amplitudes and the difference of their decay along scales are the parameters to use for defining similarities in the image. Experimental results show the potentialities of the method in terms of visual quality and mean square error, reaching the most powerful and recent de-noising schemes.
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.
References
Azzabou, N., Paragios, N., Guichard, F.: Image denosing based on adapted dictionary computation. In: Proc. of ICIP 2007, vol. III, pp. 109–112 (2007)
Balster, E.J., Zheng, Y., Ewing, R.: Feature-based wavelet shrinkage algorithm for image denoising. IEEE Transactions on Image Processing 14 (2005)
Bruni, V., Vitulano, D.: Wavelet based signal denoising via simple singularities approximation. Signal Processing, Elsevier Science 86, 859–876 (2006)
Buades, A., Coll, B., Morel, J.: A review of image denoising algorithms with a new one. SIAM Multiscale Model. Simul. 4, 490–530 (2005)
Chang, S., Yu, B., Vetterli, M.: Spatially adaptive thresholding with context modeling for image denoising. IEEE Trans. on Image Proc. 9, 1522–1530 (2000)
Donoho, D.L.: Denoising by soft thresholding. IEEE Trans. on Information Theory 41, 613–627 (1995)
Dragotti, P., Vetterli, M.: Wavelet footprints: Theory, algorithms and applications. IEEE Trans. on Signal Proc. 51, 1306–1323 (2003)
Elad, M., Aharon, M.: Image denoising via learned dictionaries and sparse representation. In: Proceedings of IEEE CVPR 2006 (2006)
Foi, A., Katkovnik, V., Egiazarian, K.: Pointwise shape adaptive dct for high quality denoising and deblocking of grayscale and color images. In: Proc. of SPIE - IS & T Electronic Imaging, vol. 6064 (2006)
Guerrero-Colon, J., Mancera, L., Portilla, J.: Image restoration using space-variant gaussian scale mixtures in overcomplete pyramids. IEEE Trans. on Image Proc. 17, 27–41 (2008)
Kervrann, C., Boulanger, J., Coupé, P.: Bayesian non local mean filter, image redundancy and adaptive dictionaries for noise removal. In: Sgallari, F., Murli, A., Paragios, N. (eds.) SSVM 2007. LNCS, vol. 4485, pp. 520–532. Springer, Heidelberg (2007)
Mallat, S., Hwang, W.: Singularity detection and processing with wavelets. IEEE Trans. on Information Theory 38 (1992)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. on PAMI 12, 629–639 (1990)
Pizurica, A., Philips, W., Lemanhieu, I., Acheroy, M.: A joint inter- and intrascale statistical model for bayesian wavelet based image denoising. IEEE Trans. on Image Proc. 11 (2002)
Sendur, L., Selesnick, I.: Bivariate shrinkage with local variance estimation. IEEE Signal Processing Letters 9, 670–684 (2002)
Wei, J.: Lebesgue anisotropic image denoising. Wiley Periodicals, Chichester (2005)
Teboul, S., Blanc-Feraud, L., Aubert, G., Barlaud, M.: Variational approach for edge-preserving regularization using coupled pde’s. IEEE Trans. on Image Proc. 7, 387–397 (1998)
Do, M.N., Vetterli, M.: Contourlets: A new directional multiresolution image representation. In: Proc. 36th Asilomar Conf. on Signals Systems and Computers, Asilomar, pp. 497–501 (2002)
Pennec, E.L., Mallat, S.: Non linear image approximation with bandelets. Tech. Rep. CMAP/ Ecole Polytechnique (2003)
Starck, J.L., Candes, E.J., Donoho, D.L.: The curvelet transform for image denoising. IEEE Trans. on Image Proc. 11, 670–684 (2002)
Coupé, P., Hellier, P., Prima, S., Kervrann, C., Barillot, C.: 3d wavelet subbands mixing for image denoising. International Journal of Biomedical Imaging (2008)
Bruni, V., Piccoli, B., Vitulano, D.: A fast computation method for time scale signal denoising. Signal, Image and Video Processing. Springer, London (2008)
Bruni, V., Piccoli, B., Vitulano, D.: Wavelet time-scale dependencies for signal and image compression. In: Proc. of IEEE Int. Conf. ISPA 2005, Zagreb, pp. 105–110 (2005)
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
Bruni, V., Vitulano, D. (2008). Image Denoising Using Similarities in the Time-Scale Plane. In: Blanc-Talon, J., Bourennane, S., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2008. Lecture Notes in Computer Science, vol 5259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88458-3_33
Download citation
DOI: https://doi.org/10.1007/978-3-540-88458-3_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88457-6
Online ISBN: 978-3-540-88458-3
eBook Packages: Computer ScienceComputer Science (R0)