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

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 378 ◽  
Author(s):  
Adisak Hanjing ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Image Restoration ◽  
Optimization Method ◽  
Convergence Result ◽  
Fixed Point Algorithm ◽  
Convergence Behavior ◽  
Lower Semi ◽  
Restoration Algorithm ◽  
Nonexpansive Operators

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.

scholarly journals Compressed sensing image restoration algorithm based on improved SURF operator

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 1033-1045
Author(s):  
Guodong Zhou ◽  
Huailiang Zhang ◽  
Raquel Martínez Lucas
Keyword(s):  
Compressed Sensing ◽  
Image Restoration ◽  
Feature Vector ◽  
Optimization Method ◽  
Image Feature ◽  
Diffusion Method ◽  
Local Similarity ◽  
Weighting Method ◽  
Data Smoothing ◽  
Restoration Algorithm

Abstract Aiming at the excellent descriptive ability of SURF operator for local features of images, except for the shortcoming of global feature description ability, a compressed sensing image restoration algorithm based on improved SURF operator is proposed. The SURF feature vector set of the image is extracted, and the vector set data is reduced into a single high-dimensional feature vector by using a histogram algorithm, and then the image HSV color histogram is extracted.MSA image decomposition algorithm is used to obtain sparse representation of image feature vectors. Total variation curvature diffusion method and Bayesian weighting method perform image restoration for data smoothing feature and local similarity feature of texture part respectively. A compressed sensing image restoration model is obtained by using Schatten-p norm, and image color supplement is performed on the model. The compressed sensing image is iteratively solved by alternating optimization method, and the compressed sensing image is restored. The experimental results show that the proposed algorithm has good restoration performance, and the restored image has finer edge and texture structure and better visual effect.

scholarly journals A Fast Fixed-Point Algorithm for Convex Minimization Problems and Its Application in Image Restoration Problems

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2619
Author(s):  
Panadda Thongpaen ◽  
Rattanakorn Wattanataweekul
Keyword(s):  
Fixed Point ◽  
Image Restoration ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Convex Minimization ◽  
Fixed Point Algorithm ◽  
Minimization Problems ◽  
Convex Minimization Problems ◽  
Weak Convergence Theorem ◽  
Inertial Technique

In this paper, we introduce a new iterative method using an inertial technique for approximating a common fixed point of an infinite family of nonexpansive mappings in a Hilbert space. The proposed method’s weak convergence theorem was established under some suitable conditions. Furthermore, we applied our main results to solve convex minimization problems and image restoration problems.

scholarly journals Iterative methods for optimization problems and image restoration

2021 ◽  
Vol 37 (3) ◽  
pp. 497-512
Author(s):  
ANANTACHAI PADCHAROEN ◽  
◽  
DUANGKAMON KITKUAN ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Image Restoration ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Minimization Problem ◽  
Convex Functions ◽  
Optimization Problems ◽  
Nonexpansive Mappings ◽  
Lower Semi

In this paper, we introduce a new accelerated iterative method for finding a common fixed point of a countable family of nonexpansive mappings in the Hilbert spaces framework. Using our main result, we obtain a new accelerated image restoration iterative method for solving a minimization problem in the form of the sum of two proper lower semi-continuous and convex functions. As applications, we apply our algorithm to solving image restoration problems.

Common Fixed Points in Modular Spaces

2018 ◽  
pp. 502 ◽  
Author(s):  
Salwa Salman Abed ◽  
Karrar Emad Abdul Sada
Keyword(s):  
Fixed Point ◽  
Weak Convergence ◽  
Fixed Point Theorems ◽  
Active Role ◽  
Common Fixed Points ◽  
Weakly Compact ◽  
Expansive Mapping ◽  
Modular Spaces ◽  
Opial’S Property ◽  
Common Fixed Point Theorems

     In this paper,there are   new considerations about the dual of a modular spaces and weak convergence. Two common fixed point theorems for a -non-expansive mapping defined on a star-shaped weakly compact subset are proved,  Here the conditions of affineness, demi-closedness and Opial's property play an active role in the proving our results.  

Image Restoration Algorithm for Single Nighttime Weakly Illuminated Haze Image

2018 ◽  
Vol 30 (3) ◽  
pp. 459
Author(s):  
Chunming Tang ◽  
Yancheng Dong ◽  
Xin Sun ◽  
Jun Lin ◽  
Zheng Lian
Keyword(s):  
Image Restoration ◽  
Restoration Algorithm

Approximating the minimum-norm fixed point of pseudocontractive mappings

2015 ◽  
Vol 08 (02) ◽  
pp. 1550036
Author(s):  
H. Zegeye ◽  
O. A. Daman
Keyword(s):  
Fixed Point ◽  
Iterative Process ◽  
Convergence Result ◽  
Monotone Mappings ◽  
Minimum Norm ◽  
Nonlinear Operators ◽  
Linear Inverse Problems ◽  
Minimization Problems ◽  
Pseudocontractive Mappings ◽  
Convex Minimization Problems

We introduce an iterative process which converges strongly to the minimum-norm fixed point of Lipschitzian pseudocontractive mapping. As a consequence, convergence result to the minimum-norm zero of monotone mappings is proved. In addition, applications to convexly constrained linear inverse problems and convex minimization problems are included. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

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