- Volume 38 Issue 5_6
DOI QR Code
FIXED-POINT-LIKE METHOD FOR A NEW TOTAL VARIATION-BASED IMAGE RESTORATION MODEL
- WON, YU JIN (Department of Mathematics, College of Natural Sciences, Chungbuk National University) ;
- YUN, JAE HEON (Department of Mathematics, College of Natural Sciences, Chungbuk National University)
- Received : 2020.05.26
- Accepted : 2020.07.30
- Published : 2020.09.30
In this paper, we first propose a new total variation-based regularization model for image restoration. We next propose a fixed-point-like method for solving the new image restoration model, and then we provide convergence analysis for the fixed-point-like method. To evaluate the feasibility and efficiency of the fixed-point-like method for the new proposed total variation-based regularization model, we provide numerical experiments for several test problems.
- A. Beck and M. Teboulle, Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems, IEEE Transactions on Image Processing 18 (2009), 2419-2433. https://doi.org/10.1109/TIP.2009.2028250
- A. Beck, First-Order Methods in Optimization, SIAM, Philadelphia, PA, 2017.
- A. Bjorck, Numerical methods for least squares problems, SIAM, Philadelphia, PA, 1996.
- J.F. Cai, S. Osher and Z. Shen, Split Bregman Methods and Frame Based Image Restoration, Multiscale Model. Simul. 8 (2009), 337-369. https://doi.org/10.1137/090753504
- R. Campagna, S. Crisci, S. Cuomo, L. Marcellino and G. Toraldo, Modification of TV-ROF denoising model based on Split Bregman iterations, Applied Mathematics and Computation 315 (2017), 453-467. https://doi.org/10.1016/j.amc.2017.08.001
- D.Q. Chen, H. Zhang and L.Z. Cheng, A Fast Fixed Point Algorithm for Total Variation Deblurring and Segmentation, Journal of Mathematical Imaging and Vision 43 (2012), 167-179. https://doi.org/10.1007/s10851-011-0298-7
- T. Goldstein and S. Osher, The Split Bregman Method for L1 Regularized Problems, SIAM Journal on Imaging Sciences 2 (2009), 323-343. https://doi.org/10.1137/080725891
- C.T. Kelly, Iterative methods for linear and nonlinear equations, SIAM, Philadelphia, USA, 1995.
- K.S. Kim and J.H. Yun, Image Restoration Using a Fixed-Point Method for a TVL2 Regularization Problem, Algorithms 13 (2020), 1-15. https://doi.org/10.3390/a13010001
- Q. Li, C.A. Micchelli, L. Shen and Y. Xu, A proximity algorithm accelerated by Gauss-Seidel iterations for L1/TV denoising models, Inverse Problems 28 (2012).
- X. Liu and L. Huang, Split Bregman iteration algorithm for total bounded variation regularization based image deblurring, Journal of Mathematical Analysis and Applications 372 (2010), 486-495. https://doi.org/10.1016/j.jmaa.2010.07.013
- J. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Am. Math. Soc. 73 (1967), 591-597. https://doi.org/10.1090/S0002-9904-1967-11761-0
- L.I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D. 60 (1992), 259-268. https://doi.org/10.1016/0167-2789(92)90242-F
- J.H. Yun, Image Deblurring Using Relaxation Iterative Methods, Journal of Algorithms and Computational Technology 13 (2019), 16 pages, Article ID 861732.
- J.H. Yun, Image denoising methods for new TVL1 models with impulse noise, Int. J. Eng. Res. Tech. 13 (2020), 686-698. https://doi.org/10.37624/IJERT/13.4.2020.686-698
- J.H. Yun and H.J. Lim, Image Restoration Using Fixed-Point-Like Methods for New TVL1 Variational Problems, Electronics 9 (2020), 17 pages, Article ID 735.