Inverse Problems and Imaging (IPI)

Multiplicative noise removal with a sparsity-aware optimization model
Pages: 949 - 974, Issue 6, December 2017

doi:10.3934/ipi.2017044      Abstract        References        Full text (4320.1K)           Related Articles

Jian Lu - College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China (email)
Lixin Shen - Department of Mathematics, Syracuse University, Syracuse, NY 13244, United States (email)
Chen Xu - College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China (email)
Yuesheng Xu - School of Data and Computer Science, Guangdong Provincial Key Lab of Computational Science, Sun Yat-sen University, Guangzhou 510275, China (email)

1 G. Aubert and J. Aujol, A variational approach to removing multiplicative noise, SIAM J. Appl. Math., 68 (2008), 925-946.       
2 R. Bamler, Principles of synthetic aperture radar, Surv. Geophys., 21 (2000), 147-157.
3 H. L. Bauschke and P. L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, AMS Books in Mathematics, Springer New York, 2011.       
4 J. M. Bioucas-Dias and M. A. T. Figueiredo, Multiplicative noise removal using variable splitting and constrained optimization, IEEE Trans. Image Process., 19 (2010), 1720-1730.       
5 M. F. C. Chesneau and J. Starck, Stein block thresholding for image denoising, Appl. Computat. Harmon. Anal., 28 (2010), 67-88.       
6 K. Dabov, A. Foi, V. Katkovnik and K. Egiazarian, Image denoising by sparse 3d transform-domain collaborative filtering, IEEE Trans. Image Process., 16 (2007), 2080-2095.       
7 D. Dai, L. Shen, Y. Xu and N. Zhang, Noisy 1-bit compressive sensing: Models and algorithms, Appl. Computat. Harmon. Anal., 40 (2016), 1-32.       
8 I. Daubechies, Ten Lectures on Wavelets, vol. 61 of CBMS Conf. Series Appl. Math., SIAM, Philadelphia, 1992.       
9 I. Daubechies, B. Han, A. Ron and Z. Shen, Framelets: MRA-based constructions of wavelet frames, Appl. Comput. Harmon. Anal., 14 (2003), 1-46.       
10 L. Denis, F. Tupin, J. Darbon and M. Sigelle, SAR image regularization with fast approximation discrete minimization, IEEE Trans. Image Process., 18 (2009), 1588-1600.       
11 Y. Dong and T. Zeng, A convex variational model for restoring blurred images with multiplicative noise, SIAM J. Imag. Sci., 6 (2013), 1598-1625.       
12 S. Durand, J. Fadili and M. Nikolova, Multiplicative noise removal using l1 fidelity on frame coefficients, J. Math. Imag. Vis., 36 (2010), 201-226.
13 J. W. Goodman, Some fundamental properties of speckle, J. Opt. Soc. of Amer., 66 (1976), 1145-1150.
14 Y. Hang, L. Moisan, M. K. Ng and T. Zeng, Multiplicative noise removal via a learned dictionary, IEEE Trans. Image Process., 21 (2012), 4534-4543.       
15 Y.-H. Huang, H. Yan and T. Zeng, Multiplicative noise removal based on unbiased box-cox transformation, Communications in Computational Physics, 22 (2017), 803-828.       
16 Y.-M. Huang, M. K. Ng and Y.-W. Wen, A new total variation method for multiplicative noise removal, SIAM J. Imag. Sci., 2 (2009), 20-40.       
17 M. Kang, S. Yun and H. Woo, Two-level convex relaxed variational model for multiplicative denoising, SIAM J. Imag. Sci., 6 (2013), 875-903.       
18 D. Lazard, Quantifier elimination: Optimal solution for two classical examples, J. Symbol. Comput., 5 (1988), 261-266.       
19 F. Li, M. K. Ng and C. Shen, Multiplicative noise removal with spatially varying regularization parameters, SIAM J. Imag. Sci., 3 (2010), 1-20.       
20 J. Lu, L. Shen, C. Xu and Y. Xu, Multiplicative noise removal in imaging: An exp-model and its fixed-point proximity algorithm, Appl. Comput. Harmon. Anal., 41 (2016), 518-539.       
21 C. A. Micchelli, L. Shen and Y. Xu, Proximity algorithms for image models: Denoising, Inverse Probl., 27 (2011), 045009(30pp).       
22 J.-J. Moreau, Fonctions convexes duales et points proximaux dans un espace hilbertien, C.R. Acad. Sci. Paris Sér. A Math., 255 (1962), 2897-2899.       
23 Y. Nesterov, Introductory Lectures on Convex Optimization, Kluwer, Boston, 2004.       
24 C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Imaging, SciTech Publishing, Raleigh, NC, 2004.
25 S. Parrilli, M. Poderico, C. V. Angelino and L. Verdoliva, A nonlocal SAR image denoising algorithm based on LLMMSE wavelet shrinkage, IEEE Trans. Geosci. Remote Sens., 50 (2012), 606-616.
26 L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), 259-268.       
27 J. M. Schmitt, S. H. Xiang and K. M. Yung, Speckle in optical coherence tomography, J. Biomed. Opt., 4 (1999), 95-105.
28 J. Shi and S. Osher, A nonlinear inverse scale space method for a convex multiplicative noise removal, SIAM J. Imag. Sci., 1 (2008), 294-321.       
29 G. Steidl and T. Teuber, Removing multiplicative noise by Douglad-Rachford splitting methods, J. Math. Imag. Vis., 36 (2010), 168-184.       
30 T. Teuber and A. Lang, Nonlocal filters for removing multiplicative noise, Proc. of SSVM, LNCS, 6667 (2012), 50-61.
31 R. F. Wagner, S. W. Smith, J. M. Sandrik and H. Lopez, Statistics of speckle in ultrasound B-scans, IEEE Trans. Sonics and Ultrason., 30 (1983), 156-163.
32 S. Yun and H. Woo, A new multiplicative denoising variational model based on m-th root transformation, IEEE Trans. Image Process., 21 (2012), 2523-2533.       

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