Abstract
This paper describes a method for de-noising images by thresholding Gabor transforms recursively. A new localized estimation of the noise standard deviation is obtained. It is shown that the algorithm converges globally using a few number of iterations. Experimental results show a remarkable improvement compared with the wavelet based de-noising methods (SureShrink and BayesShrink).
Similar content being viewed by others
References
Hirakawa K., Parks T.: Image denoising using total least squares. IEEE Trans. Image Process. 15, 2730–2742 (2006)
Burgeth B., Didas S., Florack L., Weickert J.: A generic approach to diffusion filtering of matrix fields. Computing 81, 179–197 (2007)
Schevnders, P., De Backer, S.: Wavelet denoising multi-component image using a Gaussian scale mixture model. In: Proceedings of the IEEE International Conference on Pattern Recognitions ICPR, Hong Kong, vol.~3, pp. 754–757 (2006)
Bisih N., Thanh N.: Object detection of speckle image based on curvelet transform. ARPN J. Eng. Appl. Sci. 2, 14–16 (2007)
Chaux C., Duval L., Benyahia A., Pesquest J.: A nonlinear stein based estimator for multichannel image denoising. IEEE Trans Signal Process. 56, 3855–3870 (2008)
Raphan M., SimonCelli E.: Optimal denoising in redundant representations. IEEE Trans. Image Process. 17, 1342–1352 (2008)
Bastiaans M.: Gabor’s expansion of a signal into Gaussian elementary signals. Proc. IEEE 68, 594–598 (1980)
Feichtinger, H., Srohmer, T. (eds.): Gabor Analysis and Algorithms. Birkauser, Boston (1998)
Grochenig K.: Foundation of time- frequency analysis. Birkauser, Boston (2001)
Tao D., Li X., Wu X., Maybank S.: General tensor discriminant analysis and Gabor features for Gait recognition. IEEE Trans. Pattern Anal. Mach. Intell. 29(10), 1700–1715 (2007)
Senapati S., Chakroboty S., Saha G.: Speech enhancement by joint characterization in log Gabor wavelet domain. Speech Commun. 50, 504–518 (2008)
Kong, A.: An alternative Gabor filtering scheme. IEEE 17th International Conference on Image Processing, pp. 1925–1928 (2010)
Lee T.: Image representation using 2D Gabor wavelets. IEEE Trans. Pattern Anal. Mach. Intell. 18, 959–971 (1996)
Bo, F., Zhi, H., Zheng, L.: A novel enhancement method based on Gabor filtering. Image and Signal Processing, CISP’09, 2nd International Congress on Digital Object Identifier, pp. 1–5 (2009)
Young I., Vliet L., Ginkel M.: Recursive Gabor filtering. IEEE Trans. Signal Process. 50, 2798–2805 (2002)
Zhou, Y., Zheng, Y.: Enhancement of muscle fibers in ultrasound images using Gabor filters. Ultrasonics Symposium (IUS), 2009 IEEE International Digital Object Identifier, pp. 2296–2299 (2009)
Yu W., Sommer G., Daniilidis K., Duncan J.: Using skew Gabor filter in source signal separation and local spectral orientation analysis. Image Vision Comput. 32, 377–392 (2005)
Daubechies I.: The wavelet transform, time frequency localization and signal analysis. IEEE Trans. Inf. Theory 36, 961–1004 (1990)
Walker, J., Chen, Y.: Denoising Gabor transforms. Reprint, available at: http://www.uwec.edu/walkerjs/media/DGT.pdf
Fletcher, A., Ramchandran, K., Gayol, V.: Wavelet denoising by recursive cycle spinning. In: Proceedings of the IEEE International Conference on Image Processing, Rochester, vol. 2, pp. 873–876 (2002)
Cheng, X., Hart, J., Walker, J., Chen, Y.: Time–Frequency Analysis of Musical Rhythm. Notices of the American Mathematical Society, vol. 56, No. 3, pp. 356–372 (2009)
Donoho D., Johnstone I.: Adapting to unknown smoothness via wavelet shrinkage. Am. Stat. Assoc. 90, 1200–1224 (1995)
Chipman H., Kolaczyk E., Mcculloch R.: Adaptive Bayesian wavelet shrinkage. J. Am. Stat. Assoc. 92, 1413–1421 (1997)
Stein C.: Estimation of the mean of a multivariate normal distribution. Ann. Stat. 9, 1135–1151 (1981)
Coifman, R., Donoho, D.: Translation-invariant de-noising. In: Antoniadis, A., Oppenheim, G. (eds.) Wavelets and Statistics. Springer, Berlin (1995)
Chang S., Yu B., Vetterli M.: Spatially adaptive wavelet thresholding with context modeling for image de-noising. IEEE Trans. Image Proc. 9, 1522–1531 (2000)
Smart D.: Fixed Point Theorems. Cambridge University press, Cambridge (1974)
Kreysizig E.: Introductory Functional Analysis with Applications. Wiley, New York (1978)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nabil, T. Iterative Projective Gabor Method for Images Filtering. Arab J Sci Eng 38, 2745–2753 (2013). https://doi.org/10.1007/s13369-012-0489-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13369-012-0489-6