Another look at the split common fixed point problem for demicontractive operators

Shehu, Yekini; Cholamjiak, Prasit

doi:10.1007/s13398-015-0231-9

Cited by 34 publications

(19 citation statements)

References 35 publications

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“…Furthermore, the tests show that the quantity SNR of the present algorithm is about 10% greater than that of the algorithms of Censor & Segal 6 , and Shehu & Cholamjiak. 13 This confirms that the results obtained by…”

Section: Figure 1 Original Imagessupporting

confidence: 90%

“…Comparison of recovered images by using different algorithms, when the number of iterations is 1,000. From left to right: Censor & Segal, 6 Shehu & Cholamjiak, 13 and present our algorithm show improvement over the previous algorithms reported by Censor & Segal 6 and Shehu & Cholamjiak. 13 Figure 3 shows the restored images of the present solution and is compared with available data from algorithms in 6 and 13 when n = 1, 000 used.…”

Section: Figurementioning

confidence: 53%

“…Now, we come to the conclusion that our result provides higher SNR values than those of Censor & Segal 6 and Shehu & Cholamjiak. 13 This implies that the restored images of our algorithm have the better quality and efficiency.…”

Section: Figurementioning

confidence: 85%

“…As of results when n = 1, 000 was used, the restored images degraded while SNR decreased. Moreover, the obtained results in Figure 9 showed that the proposed algorithm reduced the processing time suitably, compared to the Censor & Segal 6 and Shehu & Cholamjiak 13 algorithms where the value for was selected as 22-25 for the image of tower 1 and 18-21 for the image of tower 2. In addition, results in Figure 9 exhibited the speed of convergence for the ability of algorithms.…”

Section: Figurementioning

confidence: 97%

See 3 more Smart Citations

Inertial self‐adaptive algorithm for solving split feasible problems with applications to image restoration

Suparatulatorn

Charoensawan

Poochinapan

2019

Math Methods in App Sciences

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We introduce a new self-adaptive algorithm for applications to image restoration problems. In order to study an image restoration, we consider the algorithm that contains inertial effects and step sizes, which is independent from the norm of the bounded linear operator. With some control conditions, the strong convergence to the minimum norm solution of the algorithm is obtained. Convergence analysis of the proposed algorithm is also discussed. Moreover, numerical results of image restoration problems illustrate that the proposed algorithm is efficient and outperforms other ones. KEYWORDSdemicontractive operator, image restoration problem, inertial algorithm, self-adaptive algorithm MSC CLASSIFICATION 47J25; 65K10wherex is an original image, y is the observed image, A is a blurring matrix, and is a noise term.The split common fixed point problem has received much attention due to its applications in image reconstruction, signal processing, intensity-modulated radiation therapy, computed tomography, control theory, approximation theory, Math Meth Appl Sci. 2019;42:7268-7284.

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Section: Figure 1 Original Imagessupporting

confidence: 90%

Section: Figurementioning

confidence: 53%

Section: Figurementioning

confidence: 85%

Section: Figurementioning

confidence: 97%

See 2 more Smart Citations

Inertial self‐adaptive algorithm for solving split feasible problems with applications to image restoration

Suparatulatorn

Charoensawan

Poochinapan

2019

Math Methods in App Sciences

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“…This algorithm is known as the forward-backward algorithm, and it includes, as special cases, the gradient method [1][2][3] and the proximal algorithm [4][5][6][7]. Recently, the construction of algorithms has become a crucial technique for solving some nonlinear and optimization problems (see also [8][9][10][11][12][13][14][15]).…”

Section: Introductionmentioning

confidence: 99%

A Novel Forward-Backward Algorithm for Solving Convex Minimization Problem in Hilbert Spaces

2020

Self Cite

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In this work, we aim to investigate the convex minimization problem of the sum of two objective functions. This optimization problem includes, in particular, image reconstruction and signal recovery. We then propose a new modified forward-backward splitting method without the assumption of the Lipschitz continuity of the gradient of functions by using the line search procedures. It is shown that the sequence generated by the proposed algorithm weakly converges to minimizers of the sum of two convex functions. We also provide some applications of the proposed method to compressed sensing in the frequency domain. The numerical reports show that our method has a better convergence behavior than other methods in terms of the number of iterations and CPU time. Moreover, the numerical results of the comparative analysis are also discussed to show the optimal choice of parameters in the line search.

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An inertial method for a solution of split equality of monotone inclusion and the f$$ f $$‐fixed point problems in Banach spaces

Zegeye

Sangago

et al. 2022

Math Methods in App Sciences

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In this paper, we propose an inertial algorithm for solving split equality of monotone inclusion and 𝑓 -fixed point of Bregman relatively 𝑓 -nonexpansive mapping problems in reflexive real Banach spaces. Using the Bregman distance function, we prove a strong convergence theorem for the algorithm produced by the method in real reflexive Banach spaces. In addition, we provide some applications of our method and give numerical results to demonstrate the applicability and efficiency of the proposed method.

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Another look at the split common fixed point problem for demicontractive operators

Cited by 34 publications

References 35 publications

Inertial self‐adaptive algorithm for solving split feasible problems with applications to image restoration

Inertial self‐adaptive algorithm for solving split feasible problems with applications to image restoration

A Novel Forward-Backward Algorithm for Solving Convex Minimization Problem in Hilbert Spaces

An inertial method for a solution of split equality of monotone inclusion and the f$$ f $$‐fixed point problems in Banach spaces

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