Influence to New Formulas Gradient for Removing Impulse Noise Images

В методах сопряженных градиентов формула сопряжения часто является основной точкой концентрации. Техника сопряженных градиентов используется для решения проблем, возникающих в процессе восстановления изображения. Используя квадратичную модель, для операции будет получено совершенно новое сопряжение коэффициентов. Алгоритмы демонстрируют как локальную, так и глобальную сходимость и спуск. Численное тестирование показало, что недавно разработанный метод намного превосходит тот, который существовал до него. Недавно созданная стратегия сопряженного градиента имеет более высокую производительность, чем метод сопряженного градиента FR, который является отраслевым стандартом.

Ключевые слова

влияние на градиент формулы; свойство конвергенции; импульсное шумоподавление изображений.

Литература

1. Wei Xue, Junhong Ren, Xiao Zheng, Zhi Liu, Yueyong Lianga. A New DY Conjugate Gradient Method and Applications to Image Denoising. IEICE Transactions on Information and Systems, 2018, vol. 101, no. 12, pp. 2984-2990. DOI: 10.1587/transinf.2018EDP7210
2. Fletcher R. Practical Methods of Optimization. Chichester, N.Y., Brisbane, Toronto, Singapore, John Wiley and Sons, 2013. DOI: 10.1002/9781118723203
3. Fletcher R., Reeves C.M. Function Minimization by Conjugate Gradients. Computer Journal, 1964, vol. 7, no. 2, pp. 149-154. DOI: 10.1093/comjnl/7.2.149
4. Yasushi N., Hideaki I. Conjugate Gradient Methods using Value of Objective Function for Unconstrained Optimization. Optimization Letters, 2012, vol. 6, pp. 941-955. DOI: 10.23851/mjs.v27i5.170
5. Polak E., Ribiere G. Note sur la Convergence de Methodes de Directions Conjuguees. Revue Francaise D'Informatique et de Recherche Operationnelle. Serie Rouge, 1969, vol. 3, no. 16, pp. 35-43. (in French)
6. Wolfe P. Convergence Conditions for Ascent Methods. II: Some Corrections. Society for Industrial and Applied Mathematics Review, 1971, vol. 13, no. 2, pp. 185-188. DOI: 10.1137/1011036
7. Wolfe P. Convergence Conditions for Ascent Methods. Society for Industrial and Applied Mathematics Review, 1969, vol. 11, no. 2, pp. 226-235. DOI: 10.1137/1011036
8. Hassan B.A., Abdullah Z.M., Jabbar H.N. A Descent Extension of the Dai-Yuan Conjugate Gradient Technique. Indonesian Journal of Electrical Engineering and Computer Science, 2019, vol. 16, no. 2, pp. 661-668. DOI: 10.11591/ijeecs.v16.i2.pp661-668
9. Dai Uhong, Han Jiye, Liu Guanghui, Sun Defeng, Yin Hongxia, Yuan Ya-Xiang. Convergence Properties Of Nonlinear Conjugate Gradient Methods. Society for Industrial and Applied Mathematics. Journal on Optimization, 2000, vol. 10, no. 2, pp. 345-358. DOI: 10.1137/S1052623494268443
10. Liu Y., Storey C. Efficient Generalized Conjugate Gradient Algorithms, Part 1: Theory. Journal of Optimization Theory and Applications, 1991, vol. 69, no. 1, pp. 129-137. DOI: 10.1007/BF00940464
11. Jabbar H.N., Hassan B.A. Two-Versions of Descent Conjugate Gradient Methods for Large-Scale Unconstrained Optimization. Indonesian Journal of Electrical Engineering and Computer Science, 2021, vol. 22, no. 3, p. 1643. DOI: 10.11591/ijeecs.v22.i3.pp1643-1649
12. Hassan B.A., Younis M.S., Taha M.W., Ibrahim A.H. A New Type of Step Sizes for Unconstrained Optimization. in Journal of Physics: Conference Series, 2021, vol. 1999, no. 1, article ID: 12099. DOI: 10.1088/1742-6596/1999/1/012099
13. Stiefel E. Methods of Conjugate Gradients for Solving Linear Systems. Journal of Research of the National Bureau of Standards, 1952, vol. 49, pp. 409-435. DOI: 10.6028/JRES.049.044
14. Hassan B.A., Sulaiman R.M. A New Class of Self-Scaling for Quasi-Newton Method Based on the Quadratic Model. Indonesian Journal of Electrical Engineering and Computer Science, 2021, vol. 21, no. 3, pp. 1830-1836. DOI: 10.11591/ijeecs.v21.i3.pp1830-1836
15. Zhanga Jianzhong, Xu Chengxian. Properties and Numerical Performance of Quasi-Newton Methods with Modified Quasi-Newton Equations. Journal of Computational and Applied Mathematics, 2001, vol. 137, no. 2, pp. 269-278. DOI: 10.1016/S0377-0427(00)00713-5
16. Nazareth L. A Relationship Between the BFGS and Conjugate Gradient Algorithms and its Implications for New Algorithms. Society for Industrial and Applied Mathematics. Journal on Numerical Analysis, 1979, vol. 16, no. 5, pp. 794-800. DOI: 10.1137/0716059
17. Hassan B.A., Dahawi H.O., Younus A.S. A New Kind of Parameter Conjugate Gradient for Unconstrained Optimization. Indonesian Journal of Electrical Engineering and Computer Science, 2020, vol. 17, no. 1, p. 404. DOI: 10.11591/ijeecs.v17.i1.pp404-411
18. Abubakar A.B., Kumam P., Ibrahim A.H., Chaipunya P., Ran S.A. New Hybrid Three-Term Spectral-Conjugate Gradient Method for Finding Solutions of Nonlinear Monotone Operator Equations with Applications. Mathematics and Computers in Simulation, 2022, vol. 201, pp. 670-683. DOI: 10.1016/j.matcom.2021.07.005
19. Dai Yu-Hong, Yuan Ya-xiang. A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property. Society for Industrial and Applied Mathematics. Journal on Optimization, 1999, vol. 10, no. 1, pp. 177-182. DOI: 10.1137/S1052623497318992
20. Yu Gaohang, Huang Jinhong, Zhou Yi. A Descent Spectral Conjugate Gradient Method for Impulse Noise Removal. Applied Mathematics Letters, 2010, vol. 23, no. 5, pp. 555-560. DOI: 10.1016/j.aml.2010.01.010
21. Ibrahim A.H., Kumam P., Sun M., Chaipunya P., Abubakar A.B. Projection Method with Inertial Step for Nonlinear Equations: Application to Signal Recovery. Journal of Industrial and Management Optimization, 2022, vol. 19, no. 1, pp. 30-55. DOI: 10.3934/jimo.2021173
22. Wu Caiying, Chen Guoqing. New Type of Conjugate Gradient Algorithms for Unconstrained Optimization Problems. Journal of Systems Engineering and Electronics, 2010, vol. 21, no. 6, pp. 1000-1007. DOI: 10.3969/j.issn.1004-4132.2010.06.012
23. Andrei N. An Unconstrained Optimization Test Functions Collection. Advanced Modeling and Optimization, 2008, vol. 10, no. 1, pp. 147-161.
24. Nocedal J., Wright S.J. Numerical Optimization. N.Y., Springer, 1999. DOI: 10.1007/0-387-22742-3_18
25. Hassan B.A., Jabbar H.N., Laylani Y.A. Upscaling Parameters for Conjugate Gradient Method in Unconstrained Optimization. Journal of Interdisciplinary Mathematics, 2023, vol. 26, no. 6, pp. 1171-1180. DOI: 10.47974/JIM-1615