An algorithm for the split feasible problem and image restoration
- PDF / 1,434,460 Bytes
- 18 Pages / 439.37 x 666.142 pts Page_size
- 75 Downloads / 291 Views
An algorithm for the split feasible problem and image restoration Raweerote Suparatulatorn1,2,3 · Phakdi Charoensawan1,2,3 · Kanyuta Poochinapan1,2,3 · Supreedee Dangskul1,2,3 Received: 22 February 2020 / Accepted: 28 September 2020 © The Royal Academy of Sciences, Madrid 2020
Abstract This paper proposes an accelerated algorithm for the split common fixed point problem, based on viscosity approximation methods and inertial effects. The main result will be applied to image restoration problems. This algorithm is constructed in such a way that its step sizes and the norm of a given linear operator are not related. Under some conditions, the strong convergence of the algorithm is obtained. Numerical investigations are carried out in order to illustrate high-performance of the present work, mainly using processing duration and the signal-to-noise ratio. It is also shown that this proposed algorithm is more efficient and effective than the published algorithm by Yao et al. Keywords Split common fixed point problem · Demicontractive operator · Self-adaptive algorithm · Inertial algorithm · Image restoration problem Mathematics Subject Classification 47J25 · 47H10 · 65K10
1 Introduction Nowadays, camera technologies have become increasingly important in many aspects of modern society. Facial recognition, for instance, is a technology used to identify human faces
B
Supreedee Dangskul [email protected] Raweerote Suparatulatorn [email protected] Phakdi Charoensawan [email protected] Kanyuta Poochinapan [email protected]
1
Advanced Research Center for Computational Simulation, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2
Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
3
Centre of Excellence in Mathematics, CHE, Si Ayutthaya Rd., Bangkok 10400, Thailand 0123456789().: V,-vol
123
12
Page 2 of 18
R. Suparatulatorn et al.
based on some facial features such as shapes, skin colors or even dimples—this is widely beneficial in border control, criminal investigation, security, to mention but a few. Those recognition technologies have also been improved and applied to a wide range of sciences and industries such as agricultural management, geological exploration, and weather forecast. The petroleum industry, in particular, makes use of satellite imagery in order to locate oil wells. However, due to clouds and air pollutions, those images may not be of high quality, and hence insufficient for further analysis. Image restoration then plays a crucial role in recovery of image quality. In addition, there have been applications of image restoration in other branches of sciences and engineering such as in astronomy, medical imaging, compressive sensing, and film restoration; the reader may be referred to [1], [2], [3] and [4] for more details. Defogging techniques have been developed using mathematical machinery. A vast number of publications are devoted for image restoration improvement. For example, [5–7] offer some fast high-perf
Data Loading...
