Nonlocal Filters for Removing Multiplicative Noise
In this paper, we propose nonlocal filters for removing multiplicative noise in images. The considered filters are deduced in a weighted maximum likelihood estimation framework and the occurring weights are defined by a new similarity measure for comparing data corrupted by multiplicative noise. For the deduction of this measure we analyze a probabilistic measure recently proposed for general noise models by Deledalle et al. and study its properties in the presence of additive and multiplicative noise. Since it turns out to have unfavorable properties facing multiplicative noise we propose a new similarity measure consisting of a density specially chosen for this type of noise. The properties of our new measure are examined theoretically as well as by numerical experiments. Afterwards, it is applied to define the weights of our nonlocal filters and different adaptations are proposed to further improve the results. Throughout the paper, our findings are exemplified for multiplicative Gamma noise. Finally, restoration results are presented to demonstrate the good properties of our new filters.
KeywordsImage Patch Multiplicative Noise Additive Gaussian Noise Constant Image Noisy Pixel
Unable to display preview. Download preview PDF.
- 2.Buades, A., Coll, B., Morel, J.-M.: Online demo: Non-local means denoising, http://www.ipol.im/pub/algo/bcm_non_local_means_denoising
- 3.Buades, A., Coll, B., Morel, J.-M.: A non-local algorithm for image denoising. In: IEEE Conf. on CVPR, vol. 2, pp. 60–65 (2005)Google Scholar
- 7.Deledalle, C.-A., Tupin, F., Denis, L.: Poisson NL means: Unsupervised non local means for Poisson noise. In: Proceedings of IEEE International Conference on Image Processing, pp. 801–804 (2010)Google Scholar
- 11.Matsushita, Y., Lin, S.: A probabilistic intensity similarity measure based on noise distributions. In: IEEE Conf. Computer Vision and Pattern Recognit. (2007)Google Scholar
- 15.Teuber, T., Lang, A.: A new similarity measure for nonlocal filtering in the presence of multiplicative noise. University of Kaiserslautern (preprint, 2011)Google Scholar
- 16.Wiest-Daesslé, N., Prima, S., Coupé, P., Morrissey, S.P., Barillot, C.: Rician noise removal by non-local means filtering for low signal-to-noise ratio MRI: Applications to DT-MRI. In: Metaxas, D., Axel, L., Fichtinger, G., Székely, G. (eds.) MICCAI 2008, Part II. LNCS, vol. 5242, pp. 171–179. Springer, Heidelberg (2008)CrossRefGoogle Scholar