Fast Wavelet Image Denoising Based on Local Variance and Edge Analysis

Authors: Gaoyong Luo

Abstract:

The approach based on the wavelet transform has been widely used for image denoising due to its multi-resolution nature, its ability to produce high levels of noise reduction and the low level of distortion introduced. However, by removing noise, high frequency components belonging to edges are also removed, which leads to blurring the signal features. This paper proposes a new method of image noise reduction based on local variance and edge analysis. The analysis is performed by dividing an image into 32 x 32 pixel blocks, and transforming the data into wavelet domain. Fast lifting wavelet spatial-frequency decomposition and reconstruction is developed with the advantages of being computationally efficient and boundary effects minimized. The adaptive thresholding by local variance estimation and edge strength measurement can effectively reduce image noise while preserve the features of the original image corresponding to the boundaries of the objects. Experimental results demonstrate that the method performs well for images contaminated by natural and artificial noise, and is suitable to be adapted for different class of images and type of noises. The proposed algorithm provides a potential solution with parallel computation for real time or embedded system application.

Keywords: Edge strength, Fast lifting wavelet, Image denoising, Local variance.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081655

References:

[1] I. K. Fodor, and C. Kamath, "On denoising images using wavelet-based statistical techniques," Lawrence Livermore National Laboratory LLNL technical report, UCRL JC-142357, 2001.
[2] I. Pitas, Digital Image Processing Algorithms and Applications, John Wiley & Sons, Inc., 2000.
[3] Z. Devcic, and S. Loncaric, "SVD block processing for non-linear image noise filtering," Journal of Computing and Information Technology, Volume 7, Number 3, pp 255-259, 1999.
[4] S. Voloshynovskiy, O. Koval, and T. Pun, "Wavelet-based image denoising using non-stationary stochastic geometrical image priors," in: Proceedings of SPIE Photonics West, Electronic Imaging 2003, Image and Video Communications and Processing V, Santa Clara, CA, USA, January 20-24, 2003.
[5] S.K. Ponnappan, R.M. Narayanan, and S.E. Reichenbach, "Effects of uncorrelated and correlated noise on image information content," in: Proceedings of the International Geoscience and Remote Sensing Symposium, Sydney, Australia, 2001, pp. 1898-1900.
[6] A. Gyaourova, C. Kamath, and I. K. Fodor, "Undecimated wavelet transforms for image de-noising," Lawrence Livermore National Laboratory LLNL technical report, UCRL-ID-150931, 2002.
[7] S. Zhong, and V. Cherkassky, "Image denoising using wavelet thresholding and model selection," in: Proceedings of the IEEE International Conference on Image processing, vol.3, Vancouver, BC, Canada, 2000, pp 262-265.
[8] A.R. Weeks, Fundamentals of Electronic Image Processing, SPIE Optical Engineering Press and IEEE Press, 1996.
[9] D. Harwood, M. Subbararao, H. Hakalahti, and L. Davis, "A new class of edge preserving smoothing filters," Pattern Recognition Letters, 5:155-162, 1987.
[10] C. Garnica, F. Boochs, and M. Twardochlib, "A new approach to edgepreserving smoothing for edge extraction and image segmentation," in: Proceedings of International Archives of Photogrammetry and Remote Sensing, IAPRS Symposium, Amsterdam, The Netherlands, 2000.
[11] M. A. Schulze, and J. A. Pearce, "A morphology-based filter structure for edge-enhancing smoothing," in: Proceedings of the 1994 IEEE International Conference on Image Processing, ICIP-94, Austin, Texas, 13-16 November, 1994, pp. 530-534.
[12] D. L. Donoho, and I. M. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika, vol. 81, pp. 425-455, 1994.
[13] L. Fan, L. Fan, and C. Tan, "Wavelet diffusion for document image denoising," in: Proceedings of the Seventh International Conference on Document Analysis and Recognition, Volume II, Edinburgh, Scotland, 2003.
[14] S. Chang, B. Yu, and M. Vetterli, "Image denoising via lossy compression and wavelet thresholding," in: Proceedings of the IEEE International Conference on Image Processing, Washington, DC, October 26-29, 1997, pp 604-607.
[15] S. Chang, B. Yu, and M. Vetterli, "Spatially adaptive wavelet thresholding with context modeling for image denoising," in: Proceedings of the IEEE International Conference on Image Processing, Chicago, Illinois, October 04 - 07, 1998, pp 535-539.
[16] D. L. Donoho, "De-noising by soft-thresholding," IEEE Trans. Inform. Theory, vol. 41, pp. 613-627, 1995.
[17] S. Chang, B. Yu, and M. Vetterli, "Spatially adaptive wavelet thresholding with context modeling for image denoising," IEEE Transactions on Image Processing, Vol. 9, No. 9, pp 1522-1531, 2000.
[18] I.K. Fodor, and C. Kamath, "Denoising through wavelet shrinkage: an empirical study," Journal of Electronic Imaging, Volume 12, Issue 1, pp. 151-160, 2003.
[19] M.K. Mihcak, I. Kozintsev, K. Ramchandran, and P. Moulin, "Lowcomplexity image denoising based on statistical modeling of wavelet coefficients," IEEE Signal Process. Lett. 6 (12), pp 300-303, 1999.
[20] D. Cho, and T. D. Bui, "Multivariate statistical modeling for image denoising using wavelet transforms," Signal Processing: Image Communication 20 , pp 77-89, 2005.
[21] D. L. Donoho, and I. M. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage," Journal of the American Statistical Assoc., vol. 90, no. 432, pp.1200-1224, 1995.
[22] S. Chang, B. Yu, and M. Vetterli, "Adaptive wavelet thresholding for image denoising and compression," IEEE Transactions on Image Processing, Vol. 9, No. 9, 1532-1546, 2000.
[23] D. D. Muresan, and T. W. Parks, "Adaptive principal components and image denoising," in: Proceedings of IEEE International conference on Image processing, Vol. 1, Barcelona, Spain, 14-17 September, 2003, pp 101-104.
[24] W. Sweldens, "The lifting scheme: A custom-design construction of biorthogonal wavelets," Appl. Comput. Harmon. Anal. 3(2), 186-200, 1996.
[25] W. Sweldens, "The lifting scheme: A construction of second generation wavelets," SIAM J. Math. Anal. 29(2), 511-546, 1998.
[26] I. Daubechies, and W. Sweldens, "Factoring wavelet transforms into lifting steps," J. Fourier Anal. Appl. 4(3), 247-269, 1998.
[27] R. Vargic, "An approach to 2D wavelet transform and its use for image compression," Radioengineering, Vol. 7, No. 4, 1-6, 1998.
[28] A.R. Calderbank, I. Daubechies, W. Sweldens, and B. Yeo, "Wavelet transforms that map integers to integers," Appl. Comput. Harmon. Anal. 5(3), 332-369, 1998.
[29] A. Aldroubi, and M. Unser, Wavelets in Medicine and Biology, CRC Press, Inc., Florida, 1996.
[30] G.Y. Luo, "A novel technique of image quality objective measurement by wavelet analysis throughout the spatial frequency range," Proceedings of SPIE, Vol. 5668 Image Quality and System Performance II, R. Rasmussen, Y. Miyake, Eds, 2005, pp. 173-184.
[31] S. Saha, and R. Vemuri, "An analysis on the effect of image features on lossy coding performance," IEEE Signal Processing Letters, Volume: 7, pp 104-107, 2000.