Generalized self-adaptive algorithm for solving split common fixed point problem and its application to image restoration problem

References

• O.A. Boikanyo, A strongly convergent algorithm for the split common fixed point problem, Appl. Math. Comput. 265 (2015), pp. 844–853.
   Web of Science ®Google Scholar
• C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Probl. 20(1) (2003), pp. 103–120. doi: 10.1088/0266-5611/20/1/006
   Web of Science ®Google Scholar
• Y. Censor, Finite series-expansion reconstruction methods, Proc. IEEE 71(3) (1983), pp. 409–419. doi: 10.1109/PROC.1983.12598
   Web of Science ®Google Scholar
• Y. Censor, T. Bortfeld, B. Martin, and A. Trofimov, The split feasibility model leading to a unified approach for inversion problems in intensity-modulated radiation therapy. Technical Report 20 April: Department of Mathematics, University of Haifa, Israel, (2005).
   Google Scholar
• Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms 8(2) (1994), pp. 221–239. doi: 10.1007/BF02142692
   Google Scholar
• Y. Censor and A. Segal, The split common fixed point problem for directed operators, J. Convex. Anal. 16(2) (2009), pp. 587–600.
   Web of Science ®Google Scholar
• A. Chambolle and P.L. Lions, Image recovery via total variation minimization and related problems, Numer. Math. 76(2) (1997), pp. 167–188. doi: 10.1007/s002110050258
   Web of Science ®Google Scholar
• T.F. Chan and J.J. Shen, Image processing and analysis: variational, PDE, wavelet, and stochastic methods, Vol. 94, Siam, Philadelphia, 2005.
   Google Scholar
• H. Cui and F. Wang, Iterative methods for the split common fixed point problem in Hilbert spaces, Fixed Point Theory Appl. 2014(1) (2014), pp. 221. doi: 10.1186/1687-1812-2014-78
   Google Scholar
• P. Jailoka and S. Suantai, Split common fixed point and null point problems for demicontractive operators in Hilbert spaces, Optim. Methods Soft. 34 (2017), pp. 1–16.
   Web of Science ®Google Scholar
• C. Kanzow and Y. Shehu, Generalized Krasnoselskii Mann-type iterations for nonexpansive mappings in Hilbert spaces, Comput. Optim. Appl. 67(3) (2017), pp. 595–620. doi: 10.1007/s10589-017-9902-0
   Web of Science ®Google Scholar
• P.E. Maingé, A viscosity method with no spectral radius requirements for the split common fixed point problem, Eur. J. Oper. Res. 235(1) (2014), pp. 17–27. doi: 10.1016/j.ejor.2013.11.028
   Web of Science ®Google Scholar
• P.E. Maingé, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal. 16(7-8) (2008), pp. 899–912. doi: 10.1007/s11228-008-0102-z
   Google Scholar
• A. Moudafi, The split common fixed-point problem for demicontractive mappings, Inverse Probl. 26(5) (2010), pp. 1–6. doi: 10.1088/0266-5611/26/5/055007
   Web of Science ®Google Scholar
• M. Nikolova, A variational approach to remove outliers and impulse noise, J. Math. Imaging. Vis. 20(1-2) (2004), pp. 99–120. doi: 10.1023/B:JMIV.0000011920.58935.9c
   Web of Science ®Google Scholar
• Y. Shehu and P. Cholamjiak, Another look at the split common fixed point problem for demicontractive operators Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales, Ser. A. Matemáticas 110(1) (2016), pp. 201–218.
   Google Scholar
• Y. Shehu and O.T. Mewomo, Further investigation into split common fixed point problem for demicontractive operators, Acta. Math. Sin. Engl. Ser. 32(11) (2016), pp. 1357–1376. doi: 10.1007/s10114-016-5548-6
   Web of Science ®Google Scholar
• S. Suantai, N. Pholasa, and P. Cholamjiak, Relaxed CQ algorithms involving the inertial technique for multiple-sets split feasibility problems, Rev Real Acad Cienc Exact Fís Natural A Mate 113 (2019), pp. 1081–1099.
   Web of Science ®Google Scholar
• S. Suantai, N. Pholasa, and P. Cholamjiak, The modified inertial relaxed CQ algorithm for solving the split feasibility problems, J. Ind. Manage. Optim. 14 (2018), pp. 1595–1615.
   Web of Science ®Google Scholar
• Y.C. Tang, J.G. Peng, and L.W. Liu, A cyclic algorithm for the split common fixed point problem of demicontractive mappings in Hilbert spaces, Math. Model. Anal. 17(4) (2012), pp. 457–466. doi: 10.3846/13926292.2012.706236
   Web of Science ®Google Scholar
• N.T. Vinh, P. Cholamjiak, and S. Suantai, A new CQ algorithm for solving split feasibility problems in Hilbert spaces, Bull. Malays. Math. Sci. Soc. (2018), pp. 1–18.
   Web of Science ®Google Scholar
• F. Wang, A new iterative method for the split common fixed point problem in Hilbert spaces, Optimization 66(3) (2017), pp. 407–415. doi: 10.1080/02331934.2016.1274991
   Web of Science ®Google Scholar
• J. Weickert, Anisotropic Diffusion in Image Processing, Vol. 1, Teubner, Stuttgart, 1998, pp. 59–60.
   Google Scholar
• J. Xie, A. Liao, and Y. Lei, A new accelerated alternating minimization method for analysis sparse recovery, Signal Process. 145 (2018), pp. 167–174. doi: 10.1016/j.sigpro.2017.12.010
   Web of Science ®Google Scholar
• H.K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc. 66(1) (2002), pp. 240–256. doi: 10.1112/S0024610702003332
   Web of Science ®Google Scholar
• Y. Yao, Y.C. Liou, and M. Postolache, Self-adaptive algorithms for the split problem of the demicontractive operators, Optimization 67 (2017), pp. 1309–1319. doi: 10.1080/02331934.2017.1390747
   Web of Science ®Google Scholar
• Y. Yao, J.C. Yao, Y.C. Liou, and M. Postolache, Iterative algorithms for split common fixed points of demicontractive operators without priori knowledge of operator norms, Carpathian J. Math. 34 (2018), pp. 459–466.
   Web of Science ®Google Scholar