First Order Methods for High Resolution Image Denoising
Abstract
In this paper we are interested in comparing theperformance of some of the most relevant first order non-smoothoptimization methods applied to the Rudin, Osher and Fatemi(ROF) Image Denoising Model and a Primal-Dual Chambolle-Pock Image Denoising Model. Because of the properties of theresulting numerical schemes it is possible to handle these computationspixelwise, allowing implementations based on parallelparadigms which are helpful in the context of high resolutionimaging.
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References
T. Chan and J. Shen,Image Processing And Analysis: Variational, Pde,Wavelet, And Stochastic Methods. Philadelphia, PA, USA: Society forIndustrial and Applied Mathematics, 2005.
N. Wiener,Extrapolation, Interpolation, and Smoothing of Stationary Time Series. The MIT Press, 1964.
A. Chambolle, R. A. DeVore, N. Y. Lee, and B. J. Lucier, “Nonlin-ear wavelet image processing: Variational problems, compression, and noise removal through wavelet shrinkage,”IEEE Transactions on ImageProcessing, vol. 7, no. 3, pp. 319–335, 1998.
L. I. Rudin and S. Osher, “Total variation based image restoration withfree local constraints,”Image Processing, 1994. Proceedings. ICIP-94.,IEEE International Conference, vol. 60, 1994.
L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation basednoise removal algorithms,”Physica D: Nonlinear Phenomena, vol. 60,no. 1-4, pp. 259–268, 1992.
R. H. Chan, C.-W. Ho, and M. Nikolova, “Salt and Pepper NoiseRemoval by Median Type Noise Detectors and Detail-Preserving Reg-ularization,”IEEE Transactions on Image processing, vol. 14, no. 10,pp. 1479–1485, 2005.
M. Nikolova, “A Variational Approach to Remove Outliers and Impulse Noise,” in Journal of Mathematical Imaging and Vision, vol. 20, no.1-2, 2004, pp. 99–120.
J. Peypouquet,Convex Optimization in Normed Spaces. Springer, 2015.
S. K. S. S. Villacis David, Helenius Teemu, “Photographic dataset:playing cards,” 2017.
T. M. John Cheng, Max Grossman,Professional CUDA C Programming,1st ed. Wrox, 2014.
S. C. C. Stfan van der Walt and G. Varoquaux, “Numpy: Opensource numerical tools for Python,” 2011. [Online]. Available: http://aip.scitation.org/doi/abs/10.1109/MCSE.2011.37
Y. L. B. C. P. I. A. F. Andreas Klckner, Nicolas Pinto, “Pycuda andpyopencl: A scripting-based approach to gpu run-time code generation,”2009. [Online]. Available: https://arxiv.org/abs/0911.3456
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