Abstract
In this paper, we develop a new wavelet domain statistical model for the removal of stationary noise in images. The new model is a combination of local linear projections onto bases of Principal Components, that perform a dimension reduction of the spatial neighbourhood, while avoiding the ”curse of dimensionality”. The models obtained after projection consist of a low dimensional Gaussian Scale Mixtures with a reduced number of parameters. The results show that this technique yields a significant improvement in denoising performance when using larger spatial windows, especially on images with highly structured patterns, like textures.
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
Donoho, D.L.: De-Noising by Soft-Thresholding. IEEE Trans. Inform. Theory 41, 613–627 (1995)
Crouse, M., Nowak, R., Baraniuk, R.: Wavelet-based statistical signal processing using Hidden Markov Models. IEEE. Trans. Signal Processing 46, 886–902 (1998)
Mihçak, M.K.: Low-complexity Image Denoising based on Statistical Modeling of Wavelet Coefficients. IEEE Signal Processing Letters 6(12), 300–303 (1999)
Chang, S., Yu, B., Vetterli, M.: Spatially Adaptive Wavelet Thresholding with Context Modeling for Image Denoising. IEEE Trans. Image Process. 9, 1522–1531 (2000)
Liu, J., Moulin, P.: Complexity-Regularized Image Denoising. IEEE Trans. on Image Processing 10(6), 841–851 (2001)
Fan, G., Xia, X.: Image denoising using local contextual hidden Markov model in the wavelet domain. IEEE Signal Processing Letters 8(5), 125–128 (2001)
Pižurica, A., Philips, W., Lemahieu, I., Acheroy, M.: A joint inter- and intrascale statistical model for Bayesian wavelet based image denoising. IEEE Trans. Image Processing 11(5), 545–557 (2002)
Şendur, L., Selesnick, I.: Bivariate Shrinkage with Local Variance Estimation. IEEE Signal Processing Letters 9, 438–441 (2002)
Portilla, J., Strela, V., Wainwright, M., Simoncelli, E.: Image denoising using Gaussian Scale Mixtures in the Wavelet Domain. IEEE Trans. Image Processing 12, 1338–1351 (2003)
Pižurica, A., Philips, W.: Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising. IEEE Trans. Image Process 15(3), 654–665 (2006)
Portilla, J.: Full Blind Denoising through Noise Covariance Estimation using Gaussian Scale Mixtures in the Wavelet Domain. In: Proc. Int. Conf. on Image Processing (ICIP), vol. 2, pp. 1217–1220 (2004)
Bellman, R.E.: Adaptive Control Processes: A Guided Tour. Princeton University Press, Princeton, NJ (1961)
Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press, Oxford (1995)
Comaniciu, D., Meer, P.: Mean Shift: A Robust Approach toward Feature Space Analysis. IEEE Trans. Pattern Analysis Machine Intell. 24(5), 603–619 (2002)
Jolliffe, I.T.: Principal Component Analysis. Springer, Heidelberg (1986)
Muresan, D.D., Parks, T.W.: Adaptive Principal Components and Image Denoising. In: Proc. Int. Conf. on Image Processing (ICIP) (2003)
Goossens, B., Pižurica, A., Philips, W.: Noise Reduction of Images with Correlated Noise in the Complex Wavelet Domain. In: IEEE BENELUX/DSP Valley Signal Processing Symposium SPS-DARTS, Antwerp, IEEE, Los Alamitos (2007)
Wainwright, M.J., Simoncelli, E.P., Willsky, A.S: Random Cascades on Wavelet Trees and their use in modeling and analyzing natural images. Applied Computational and Harmonic Analysis 11(1), 89–123 (2001)
Selesnick, I.W.: Laplace Random Vectors, Gaussian Noise, and the Generalized Incomplete Gamma Function. In: Proc. Int. Conf. on Image Processing (ICIP), pp. 2097–2100 (2006)
Srivastava, A., Liu, X., Grenander, U.: Universal Analytical Forms for Modeling Image Probabilities. IEEE Trans. Pattern Analysis and Machine Intelligence 24(9), 1200–1214 (2002)
Tipping, M.E., Bishop, C.M.: Mixtures of Probabilistic Principal Component Analysers. Neural Computation 11(2), 443–482 (1999)
Dempster, A., Laird, N., Rubin, D.: Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B 19(1), 1–38 (1977)
Kingsbury, N.G.: Complex Wavelets for Shift Invariant Analysis and Filtering of Signals. Journal of Applied and Computational Harmonic Analysis 10(3), 234–253 (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Goossens, B., Pižurica, A., Philips, W. (2007). Noise Removal from Images by Projecting onto Bases of Principal Components. In: Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P. (eds) Advanced Concepts for Intelligent Vision Systems. ACIVS 2007. Lecture Notes in Computer Science, vol 4678. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74607-2_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-74607-2_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74606-5
Online ISBN: 978-3-540-74607-2
eBook Packages: Computer ScienceComputer Science (R0)