Inertial viscosity forward–backward splitting algorithm for monotone inclusions and its application to image restoration problems

Kitkuan, Duangkamon; Martínez-Moreno, Juan; Sitthithakerngkiet, Kanokwan

doi:10.1080/00207160.2019.1649661

Cited by 21 publications

(25 citation statements)

References 20 publications

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“…e different colors of light in nature are electromagnetic waves of different frequencies, and the different colors people observe are the result of the human brainʼs eye perceiving electromagnetic waves of different frequencies as different colors. It is not intuitive for the Complexity human eye visual perception system to distinguish various colors in the spectrum according to their wavelengths [27][28][29][30][31][32][33].…”

Section: Artistic Color Virtual Reality Realization Modelmentioning

confidence: 99%

Artistic Color Virtual Reality Implementation Based on Similarity Image Restoration

Zhu

2021

Complexity

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In this paper, exploratory and innovative research is done on the implementation technique of artistic color virtual reality for similarity image recovery. Based on similarity images, a nonlocal natural image before the regular term is proposed to deal with the single-image blind deblurring problem. This paper designs a new artistic color virtual reality realization technology based on similarity image restoration, which exploits the low-rank property between nonlocal similarity blocks in images and combines a strong convex term to enhance the convexity of the artistic color virtual reality model. We analyze virtual reality interaction design from the perspective of art color design, sort out the concept and content of design, analyze the elements, design principles, and evaluation criteria included in virtual reality interaction art color design, and explore the conceptual principles of virtual reality interaction art color design. A full understanding of the characteristics of the medium of the virtual reality interaction can help us to better use this medium as a tool to create works that aim to bring higher quality and experiential feeling with a perceptual communication method that is closer to natural interaction. Combining the power of technology, artistic colourful thinking, and a design approach paves the way forward. The study shows that virtual reality technology can effectively improve the status quo and promote the cultivation of professional practice ability in art color design, which is conducive to the cultivation of applied design talents.

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Section: Artistic Color Virtual Reality Realization Modelmentioning

confidence: 99%

Artistic Color Virtual Reality Implementation Based on Similarity Image Restoration

Zhu

2021

Complexity

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“…In the algorithm (4), operators A and B are usually called the forward operator and the backward operator, respectively. For more details about forward-backward methods that have been constructed and considered to solve the inclusion problem (3), the reader is directed to [2,9,11,[24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

“…They proved that the sequence {x n } generated by the algorithm (8) converges weakly to a solution of the monotone inclusion problem (3) with some conditions. Kitkuan and Kumam [26] combined the forward-backward splitting method (4) with the viscosity approximation method [37] for solving the monotone inclusion problem (3). It is called the inertial viscosity forward-backward splitting algorithm, which is defined as:…”

Section: Introductionmentioning

confidence: 99%

Modified Tseng’s Method with Inertial Viscosity Type for Solving Inclusion Problems and Its Application to Image Restoration Problems

Kaewyong

Sitthithakerngkiet

2021

Mathematics

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In this paper, we study a monotone inclusion problem in the framework of Hilbert spaces. (1) We introduce a new modified Tseng’s method that combines inertial and viscosity techniques. Our aim is to obtain an algorithm with better performance that can be applied to a broader class of mappings. (2) We prove a strong convergence theorem to approximate a solution to the monotone inclusion problem under some mild conditions. (3) We present a modified version of the proposed iterative scheme for solving convex minimization problems. (4) We present numerical examples that satisfy the image restoration problem and illustrate our proposed algorithm’s computational performance.

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“…For instance, these problems are applicable to solving convex programming, the minimization problem, variational inequalities, and the split feasibility problem. As a result, some applications of such problems are able to be taken into consideration, such as machine learning, the signal recovery problem, the image restoration problem, sensor networks in computerized tomography and data compression, and intensity modulated radiation therapy treatment planning, see [1][2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the solution set for this problem is (A + B) −1 (0) ∩ Fix(S). In literature, a number of tools have been brought to investigate the inclusion problems, see [7,[10][11][12][13]. One of the most popular methods, called the forward-backward splitting method, was suggested by Lions and Mercier [14], and Passty [15].…”

Section: Introductionmentioning

confidence: 99%

Tseng Type Methods for Inclusion and Fixed Point Problems with Applications

Suparatulatorn

Khemphet

2019

Mathematics

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An algorithm is introduced to find an answer to both inclusion problems and fixed point problems. This algorithm is a modification of Tseng type methods inspired by Mann’s type iteration and viscosity approximation methods. On certain conditions, the iteration obtained from the algorithm converges strongly. Moreover, applications to the convex feasibility problem and the signal recovery in compressed sensing are considered. Especially, some numerical experiments of the algorithm are demonstrated. These results are compared to those of the previous algorithm.

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Inertial viscosity forward–backward splitting algorithm for monotone inclusions and its application to image restoration problems

Cited by 21 publications

References 20 publications

Artistic Color Virtual Reality Implementation Based on Similarity Image Restoration

Artistic Color Virtual Reality Implementation Based on Similarity Image Restoration

Modified Tseng’s Method with Inertial Viscosity Type for Solving Inclusion Problems and Its Application to Image Restoration Problems

Tseng Type Methods for Inclusion and Fixed Point Problems with Applications

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