Split common fixed point problems for demicontractive operators

Padcharoen, Anantachai; Kumam, Poom; Cho, Yeol Je

doi:10.1007/s11075-018-0605-0

Cited by 27 publications

(11 citation statements)

References 61 publications

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“…Recently, the split feasibility problem has been apllied to approximation theory, signal processing, image recovery, control theory, biomedical engineering, geophysics and communications by many authors. Refer to the papers [3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing

2019

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In 2014, Cui and Wang constructed an algorithm for demicontractive operators and proved some weak convergence theorems of their proposed algorithm to show the existence of solutions for the split common fixed point problem without using the operator norm. By Cui and Wang’s motivation, in 2015, Boikanyo constructed also a new algorithm for demicontractive operators and obtained some strong convergence theorems for this problem without using the operator norm. In this paper, we consider a viscosity iterative algorithm in Boikanyo’s algorithm to approximate to a solution of this problem and prove some strong convergence theorems of our proposed algorithm to a solution of this problem. Finally, we apply our main results to some applications, signal processing and others and compare our algorithm with five algorithms such as Cui and Wang’s algorithm, Boikanyo’s algorithm, forward-backward splitting algorithm and the fast iterative shrinkage-thresholding algorithm (FISTA).

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Section: Introductionmentioning

confidence: 99%

A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing

2019

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“…After that, the SCFP (1) for demicontractive operators has been studied by many researchers. [8][9][10][11][12] The lately result was the strong convergence of the SCFP (1) for two demicontractive operators in real Hilbert spaces. This has been performed by Shehu and Cholamjiak 13 as follows: Theorem 1.…”

Section: Introductionmentioning

confidence: 99%

“…It has the step‐size that relies on the norm of the bounded linear operator A . After that, the SCFP for demicontractive operators has been studied by many researchers …”

Section: Introductionmentioning

confidence: 99%

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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“…This problem includes, as special cases, convex programming, variational inequalities, split feasibility problem and minimization problem [1][2][3][4][5][6][7]. To be more precise, some concrete problems in machine learning, image processing [4,5], signal processing and linear inverse problem can be modeled mathematically as the form in Equation (1). Signal processing and numerical optimization are independent scientific fields that have always been mutually influencing each other.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Operators as Concerns Convex Programming and Applied to Signal Processing

Padcharoen

Sukprasert

2019

Mathematics

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Splitting methods have received a lot of attention lately because many nonlinear problems that arise in the areas used, such as signal processing and image restoration, are modeled in mathematics as a nonlinear equation, and this operator is decomposed as the sum of two nonlinear operators. Most investigations about the methods of separation are carried out in the Hilbert spaces. This work develops an iterative scheme in Banach spaces. We prove the convergence theorem of our iterative scheme, applications in common zeros of accretive operators, convexly constrained least square problem, convex minimization problem and signal processing.

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Split common fixed point problems for demicontractive operators

Cited by 27 publications

References 61 publications

A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing

A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing

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

Nonlinear Operators as Concerns Convex Programming and Applied to Signal Processing

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