Inertial forward-backward splitting method in Banach spaces with application to compressed sensing

Cholamjiak, Prasit; Shehu, Yekini

doi:10.21136/am.2019.0323-18

Cited by 51 publications

(30 citation statements)

References 36 publications

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“…It is well-known that fixed point theory has relevant applications in many branches of analysis [1][2][3][4][5][6][7][8][9] and it can be applied to solving many areas of science and applied science, engineering, economics and medicine, such as image/signal processing [10][11][12][13][14][15][16][17] and modeling intensity modulated radiation theory treatment planning [18][19][20]. Many real life problems can be equivalently formulated as fixed point problems, meaning that one has to find a fixed point of some operators.…”

Section: Introductionmentioning

confidence: 99%

A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method

Hanjing

Suantai

2020

Mathematics

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In this paper, a new accelerated fixed point algorithm for solving a common fixed point of a family of nonexpansive operators is introduced and studied, and then a weak convergence result and the convergence behavior of the proposed method is proven and discussed. Using our main result, we obtain a new accelerated image restoration algorithm, called the forward-backward modified W-algorithm (FBMWA), for solving a minimization problem in the form of the sum of two proper lower semi-continuous and convex functions. As applications, we apply the FBMWA algorithm to solving image restoration problems. We analyze and compare convergence behavior of our method with the others for deblurring the image. We found that our algorithm has a higher efficiency than the others in the literature.

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Section: Introductionmentioning

confidence: 99%

A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method

Hanjing

Suantai

2020

Mathematics

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“…where A and B are monotone mappings. For solving problem (7), several authors have studied different iterative schemes (see, e.g., [6][7][8][9][10][11][12][13][14][15][16] and references therein). The most attractive methods for solving the inclusion problem (7) are the Peaceman-Rachford and Douglas-Rachford iterative methods.…”

Section: Introductionmentioning

confidence: 99%

A strong convergence theorem for a zero of the sum of a finite family of maximally monotone mappings

Wega

Zegeye

Boikanyo

2020

Demonstratio Mathematica

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AbstractThe purpose of this article is to study the method of approximation for zeros of the sum of a finite family of maximally monotone mappings and prove strong convergence of the proposed approximation method under suitable conditions. The method of proof is of independent interest. In addition, we give some applications to the minimization problems and provide a numerical example which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

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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%

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 forward-backward splitting method in Banach spaces with application to compressed sensing

Cited by 51 publications

References 36 publications

A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method

A Fast Image Restoration Algorithm Based on a Fixed Point and Optimization Method

A strong convergence theorem for a zero of the sum of a finite family of maximally monotone mappings

Tseng Type Methods for Inclusion and Fixed Point Problems with Applications

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