Removing Multiplicative Noise by Douglas-Rachford Splitting Methods
Journal of Mathematical Imaging and Vision
Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients
Journal of Mathematical Imaging and Vision
A Fast Hybrid Algorithm for Large-Scale l1-Regularized Logistic Regression
The Journal of Machine Learning Research
A weberized total variation regularization-based image multiplicative noise removal algorithm
EURASIP Journal on Advances in Signal Processing
Proceedings of the 2011 International Conference on Communication, Computing & Security
Multiplicative Noise Removal with Spatially Varying Regularization Parameters
SIAM Journal on Imaging Sciences
Primal and Dual Bregman Methods with Application to Optical Nanoscopy
International Journal of Computer Vision
Multiplicative noise removal via a novel variational model
Journal on Image and Video Processing - Special issue on emerging methods for color image and video quality enhancement
Fast algorithm for multiplicative noise removal
Journal of Visual Communication and Image Representation
A convex relaxation method for computing exact global solutions for multiplicative noise removal
Journal of Computational and Applied Mathematics
Fast reduction of speckle noise in real ultrasound images
Signal Processing
Total variation regularization algorithms for images corrupted with different noise models: a review
Journal of Electrical and Computer Engineering
An effective dual method for multiplicative noise removal
Journal of Visual Communication and Image Representation
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We are motivated by a recently developed nonlinear inverse scale space method for image denoising [M. Burger, G. Gilboa, S. Osher, and J. Xu, Commun. Math. Sci., 4 (2006), pp. 179-212; M. Burger, S. Osher, J. Xu, and G. Gilboa, in Variational, Geometric, and Level Set Methods in Computer Vision, Lecture Notes in Comput. Sci. 3752, Springer, Berlin, 2005, pp. 25-36], whereby noise can be removed with minimal degradation. The additive noise model has been studied extensively, using the Rudin-Osher-Fatemi model [L. I. Rudin, S. Osher, and E. Fatemi, Phys. D, 60 (1992), pp. 259-268], an iterative regularization method [S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, Multiscale Model. Simul., 4 (2005), pp. 460-489], and the inverse scale space flow [M. Burger, G. Gilboa, S. Osher, and J. Xu, Commun. Math. Sci., 4 (2006), pp. 179-212; M. Burger, S. Osher, J. Xu, and G. Gilboa, in Variational, Geometric, and Level Set Methods in Computer Vision, Lecture Notes in Comput. Sci. 3752, Springer, Berlin, 2005, pp. 25-36]. However, the multiplicative noise model has not yet been studied thoroughly. Earlier total variation models for the multiplicative noise cannot easily be extended to the inverse scale space, due to the lack of global convexity. In this paper, we review existing multiplicative models and present a new total variation framework for the multiplicative noise model, which is globally strictly convex. We extend this convex model to the nonlinear inverse scale space flow and its corresponding relaxed inverse scale space flow. We demonstrate the convergence of the flow for the multiplicative noise model, as well as its regularization effect and its relation to the Bregman distance. We investigate the properties of the flow and study the dependence on flow parameters. The numerical results show an excellent denoising effect and significant improvement over earlier multiplicative models.