Double Tseng’s Algorithm with Inertial Terms for Inclusion Problems and Applications in Image Deblurring

In this research paper, we present a novel theoretical technique, referred to as the double Tseng’s algorithm with inertial terms, for finding a common solution to two monotone inclusion problems. Developing the double Tseng’s algorithm in this manner not only comprehensively expands theoretical kno...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics (Basel) 2024-10, Vol.12 (19), p.3138
Main Authors: Thammasiri, Purit, Berinde, Vasile, Petrot, Narin, Ungchittrakool, Kasamsuk
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Convexity
Euclidean space
forward–backward algorithm
Hilbert space
image deblurring problem
Image processing
Inertia (Mechanics)
Mathematical analysis
Methods
monotone inclusion problem
Noise measurement
Signal processing
Tseng-type algorithm
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this research paper, we present a novel theoretical technique, referred to as the double Tseng’s algorithm with inertial terms, for finding a common solution to two monotone inclusion problems. Developing the double Tseng’s algorithm in this manner not only comprehensively expands theoretical knowledge in this field but also provides advantages in terms of step-size parameters, which are beneficial for tuning applications and positively impact the numerical results. This new technique can be effectively applied to solve the problem of image deblurring and offers numerical advantages compared to some previously related results. By utilizing certain properties of a Lipschitz monotone operator and a maximally monotone operator, along with the identity associated with the convexity of the quadratic norm in the framework of Hilbert spaces, and by imposing some constraints on the scalar control conditions, we can achieve weak convergence to a common zero point of the sum of two monotone operators. To demonstrate the benefits and advantages of this newly proposed algorithm, we performed numerical experiments to measure the improvement in the signal–to–noise ratio (ISNR) and the structural similarity index measure (SSIM). The results of both numerical experiments (ISNR and SSIM) demonstrate that our new algorithm is more efficient and has a significant advantage over the relevant preceding algorithms.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12193138