Abstract
Partial Differential equations (PDE), wavelets-based methods and neighborhood filters were proposed as locally adaptive machines for noise removal. Recently, Buades, Coll and Morel proposed the Non-Local (NL-) means filter for image denoising. This method replaces a noisy pixel by the weighted average of other image pixels with weights reflecting the similarity between local neighborhoods of the pixel being processed and the other pixels. The NL-means filter was proposed as an intuitive neighborhood filter but theoretical connections to diffusion and non-parametric estimation approaches are also given by the authors. In this paper we propose another bridge, and show that the NL-means filter also emerges from the Bayesian approach with new arguments. Based on this observation, we show how the performance of this filter can be significantly improved by introducing adaptive local dictionaries and a new statistical distance measure to compare patches. The new Bayesian NL-means filter is better parametrized and the amount of smoothing is directly determined by the noise variance (estimated from image data) given the patch size. Experimental results are given for real images with artificial Gaussian noise added, and for images with real image-dependent noise.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Awate, S.P., Whitaker, R.T.: Higher-order image statistics for unsupervised, information-theoretic, adaptive, image filtering. In: CVPR’05, San Diego (2005)
Guichard, F., Paragios, N., Azzabou, N.: Random Walks, Constrained Multiple Hypothesis Testing and Image Enhancement. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3951, pp. 379–390. Springer, Heidelberg (2006)
Barash, D., Comaniciu, D.: A Common framework for nonlinear diffusion, adaptive smoothing, bilateral filtering and mean shift. Image Vis. Comp. 22, 73–81 (2004)
Buades, A., Coll, B., Morel, J.M.: A review of image denoising methods, with a new one. Multiscale Modeling and Simulation 4, 490–530 (2005)
Buades, A., Coll, B., Morel, J.M.: The staircasing effect in neighborhood filters and its solution. IEEE T. Image Process. 15 (2006)
Bunea, F., Nobel, A.B.: Sequential procedures for aggregating arbitrary estimators of a conditional mean (under revision) (2005)
Coupé, P., Yger, P., Barillot, C.: Fast non-local means denoising for 3D MR images. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4190, Springer, Heidelberg (2006)
Criminisi, A., Pérez, P., Toyama, K.: Region filling and object removal by exemplar-based inpainting. IEEE T. Image Process. 13, 1200–1212 (2004)
De Bonet, J.S.: Noise reduction through detection of signal redundancy. Rethinking Artificial Intelligence, MIT AI Lab. (1997)
Dabov, K., et al.: Image denoising with block-matching and 3D filtering. In: Electronic Imaging’06, San Jose, California USA. Proc. of SPIE, vol. 6064, no. 6064A-30 (2006)
Efros, A., Leung, T.: Texture synthesis by non-parametric sampling. In: ICCV’99, Kerkyra (1999)
Elad, M.: On the bilateral filter and ways to improve it. IEEE T. Image Process. 11, 1141–1151 (2002)
Elad, M., Aharon, M.: Image denoising via learned dictionaries and sparse representation. In: CVPR’06, New York (2006)
Faraji, H., MacLean, J.W.: CCD noise removal in digital images. IEEE T. Image Process. 15(9), 2676–2685 (2006)
Geman, D., et al.: Boundary detection by constrained optimization. IEEE T. Patt. Anal. Mach. Intell. 12, 609–628 (1990)
Gilboa, G., Osher, S.: Nonlocal linear image regularization and supervised segmentation. UCLA CAM Report 06-47 (2006)
Godtliebsen, F., Spjotvoll, E., Marron, J.S.: A nonlinear Gaussian filter applied to images with discontinuities. J. Nonparametric Stat. 8, 21–43 (1997)
Hirakawa, K., Parks, T.W.: Image denoising using total least squares. IEEE T. Image Process. 15(9), 2730–2742 (2006)
Katkovnik, V., Egiazarian, K., Astola, J.: Adaptive window size image denoising based on intersection of confidence intervals (ICI) rule. J. Math. Imag. Vis. 16, 223–235 (2002)
Kervrann, C., Heitz, F.: A Markov random field model-based approach to unsupervised texture segmentation using local and global spatial statistics. IEEE T. Image Process. 4, 856–862 (1995)
Kervrann, C., Boulanger, J.: Unsupervised patch-based image regularization and representation. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3951, Springer, Heidelberg (2006)
Kinderman, S., Osher, S., Jones, P.W.: Deblurring and denoising of images by nonlocal functionals. Multiscale Modeling and Simulation 4, 1091–1115 (2005)
Lee, J.S.: Digital image smoothing and the sigma filter. Comp. Vis. Graph. Image Process. 24, 255–269 (1983)
Loupas, T., McDicken, W.N., Allan, P.L.: An adaptive weighted median filter for speckle suppression inmedical ultrasonic images. IEEE T. Circ. Syst. 36, 129–135 (1989)
Lukin, A.: A multiresolution approach for improving quality of image denoising algorithms. In: ICASSP’06, Toulouse (2006)
Mahmoudi, M., Sapiro, G.: Fast image and video denoising via nonlocal means of similar neighborhoods. IEEE Signal Processing Letters 12(12), 839–842 (2005)
Mrazek, P., Weickert, J., Bruhn, A.: On robust estimation and smoothing with spatial and tonal kernels. Preprint 51, U. Bremen (2004)
Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and variational problems. Comm. Pure and Appl. Math. 42, 577–685 (1989)
Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE T. Patt. Anal. Mach. Intell. 12, 629–639 (1990)
Polzehl, J., Spokoiny, V.: Adaptive weights smoothing with application to image restoration. J. Roy. Stat. Soc. B 62, 335–354 (2000)
Portilla, J., et al.: Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE T. Image Process. 12, 1338–1351 (2003)
Roth, S., Black, M.J.: Fields of experts: a framework for learning image priors with applications. In: CVPR’05, San Diego (2005)
Rudin, L., Osher, S., Fatemi, E.: Nonlinear Total Variation based noise removal algorithms. Physica D 60(1-4), 259–268 (1992)
Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: ICCV’98, Bombay (1998)
Tschumperlé, D.: Curvature-preserving regularization of multi-valued images using PDE’s. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3951, Springer, Heidelberg (2006)
Wang, Z., Zhang, D.: Restoration of impulse noise corrupted images using long-range correlation. IEEE Signal Processing Letters 5, 4–6 (1998)
Weickert, J.: Anisotropic Diffusion in Image Processing. Teubner-Verlag, Stuttgart (1998)
van de Weijer, J., van den Boomgaard, R.: Local mode filtering. In: CVPR’01, Kauai (2001)
Zhang, D., Wang, Z.: Image information restoration based on long-range correlation. IEEE T. Circ. Syst. Video Technol. 12, 331–341 (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Kervrann, C., Boulanger, J., Coupé, P. (2007). Bayesian Non-local Means Filter, Image Redundancy and Adaptive Dictionaries for Noise Removal. In: Sgallari, F., Murli, A., Paragios, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer Science, vol 4485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72823-8_45
Download citation
DOI: https://doi.org/10.1007/978-3-540-72823-8_45
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72822-1
Online ISBN: 978-3-540-72823-8
eBook Packages: Computer ScienceComputer Science (R0)