A NEW APPROACH FOR DENOISING IMAGES BASED ON WEIGHTS OPTIMIZATION
Qiyu Jin, Ion Grama, Quansheng Liu
2012
Abstract
We propose a new algorithm to restore an image contaminated by the Gaussian white noise. Our approach is based on the weighted average of the observations in a neighborhood as in the case of the Non-Local Means Filter. But in contrast to the Non-Local Means Filter, we choose the weights by minimizing a tight upper bound of the Mean Square Error. Our theoretical results show that some ”oracle” weights defined by a triangular kernel are optimal. To construct a computable filter the ”oracle” weights are replaced by some estimates. The implementation of the proposed algorithm is straightforward. The simulations show that our approach is very competitive.
References
- Aharon, M., Elad, M., and Bruckstein, A. (2006). rmksvd: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process., 54(11):4311-4322.
- Buades, A., Coll, B., Morel, J., et al. (2005). A review of image denoising algorithms, with a new one. SIAM Journal on Multiscale Modeling and Simulation, 4(2):490-530.
- Buades, T., Lou, Y., Morel, J., and Tang, Z. (2009). A note on multi-image denoising. In Int. workshop on Local and Non-Local Approximation in Image Processing, pages 1-15.
- Dabov, K., Foi, A., Katkovnik, V., and Egiazarian, K. (2007). Image denoising by sparse 3-D transformdomain collaborative filtering. IEEE Trans. Image Process., 16(8):2080-2095.
- Donoho, D. and Johnstone, J. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81(3):425.
- Foi, A., Katkovnik, V., Egiazarian, K., and Astola, J. (2004). A novel anisotropic local polynomial estimator based on directional multiscale optimizations . In Proc. 6th IMA int. conf. math. in signal processing, pages 79-82.
- Hammond, D. and Simoncelli, E. (2008). Image modeling and denoising with orientation-adapted gaussian scale mixtures. IEEE Trans. Image Process., 17(11):2089- 2101.
- Hirakawa, K. and Parks, T. (2006). Image denoising using total least squares. IEEE Trans. Image Process., 15(9):2730-2742.
- Katkovnik, V., Foi, A., Egiazarian, K., and Astola, J. (2010). From local kernel to nonlocal multiple-model image denoising. Int. J. Comput. Vis., 86(1):1-32.
- Kervrann, C. and Boulanger, J. (2008). Local adaptivity to variable smoothness for exemplar-based image regularization and representation. Int. J. Comput. Vis., 79(1):45-69.
- Lou, Y., Zhang, X., Osher, S., and Bertozzi, A. (2010). Image recovery via nonlocal operators. J. Sci. Comput., 42(2):185-197.
- Nazin, A., Roll, J., Ljung, L., and Grama, I. (2008). Direct weight optimization in statistical estimation and system identification. System Identification and Control Problems (SICPRO08), Moscow.
- Polzehl, J. and Spokoiny, V. (2006). Propagation-separation approach for local likelihood estimation. Probab. Theory Rel. Fields, 135(3):335-362.
- Roth, S. and Black, M. (2009). Fields of experts. Int. J. Comput. Vision, 82(2):205-229.
- Sacks, J. and Ylvisaker, D. (1978). Linear estimation for approximately linear models. Ann. Stat., 6(5):1122- 1137.
- Tomasi, C. and Manduchi, R. (1998). Bilateral filtering for gray and color images. In Proc. Int. Conf. Computer Vision, pages 839-846.
- Yaroslavsky, L. P. (1985). Digital picture processing. An introduction. In Springer-Verlag, Berlin.
Paper Citation
in Harvard Style
Jin Q., Grama I. and Liu Q. (2012). A NEW APPROACH FOR DENOISING IMAGES BASED ON WEIGHTS OPTIMIZATION . In Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2012) ISBN 978-989-8565-03-7, pages 112-117. DOI: 10.5220/0003846001120117
in Bibtex Style
@conference{visapp12,
author={Qiyu Jin and Ion Grama and Quansheng Liu},
title={A NEW APPROACH FOR DENOISING IMAGES BASED ON WEIGHTS OPTIMIZATION},
booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2012)},
year={2012},
pages={112-117},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003846001120117},
isbn={978-989-8565-03-7},
}
in EndNote Style
TY - CONF
JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2012)
TI - A NEW APPROACH FOR DENOISING IMAGES BASED ON WEIGHTS OPTIMIZATION
SN - 978-989-8565-03-7
AU - Jin Q.
AU - Grama I.
AU - Liu Q.
PY - 2012
SP - 112
EP - 117
DO - 10.5220/0003846001120117