scholarly journals An Improved Alternating CQ Algorithm for Solving Split Equality Problems

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3313
Author(s):  
Yan-Juan He ◽  
Li-Jun Zhu ◽  
Nan-Nan Tan
Keyword(s):  
Signal Processing ◽  
Weak Convergence ◽  
Medical Image ◽  
Phase Retrieval ◽  
Scientific Field ◽  
Iterative Sequence ◽  
Split Equality Problem ◽  
Cq Algorithm ◽  
Equality Problem ◽  
Medical Image Reconstruction

The CQ algorithm is widely used in the scientific field and has a significant impact on phase retrieval, medical image reconstruction, signal processing, etc. Moudafi proposed an alternating CQ algorithm to solve the split equality problem, but he only obtained the result of weak convergence. The work of this paper is to improve his algorithm so that the generated iterative sequence can converge strongly.

scholarly journals Modified Projection Algorithms for Solving the Split Equality Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qiao-Li Dong ◽  
Songnian He
Keyword(s):  
Convex Sets ◽  
Applied Mathematics ◽  
The Self ◽  
Projection Algorithm ◽  
Projection Algorithms ◽  
Split Equality Problem ◽  
Relaxation Scheme ◽  
Convergence Results ◽  
Cq Algorithm ◽  
Equality Problem

The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two half-spaces in each iteration. We further propose a relaxation scheme for the self-adaptive projection algorithm by using projections onto half-spaces instead of those onto the original convex sets, which is much more practical. Weak convergence results for both algorithms are analyzed.

scholarly journals Convergence rate analysis of an iterative algorithm for solving the multiple-sets split equality problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shijie Sun ◽  
Meiling Feng ◽  
Luoyi Shi
Keyword(s):  
Convergence Rate ◽  
Iterative Algorithm ◽  
Sufficient Conditions ◽  
Linear Convergence ◽  
Regularity Property ◽  
Step Size ◽  
Bounded Linear ◽  
Split Equality Problem ◽  
Linear Convergence Rate ◽  
Equality Problem

Abstract This paper considers an iterative algorithm of solving the multiple-sets split equality problem (MSSEP) whose step size is independent of the norm of the related operators, and investigates its sublinear and linear convergence rate. In particular, we present a notion of bounded Hölder regularity property for the MSSEP, which is a generalization of the well-known concept of bounded linear regularity property, and give several sufficient conditions to ensure it. Then we use this property to conclude the sublinear and linear convergence rate of the algorithm. In the end, some numerical experiments are provided to verify the validity of our consequences.

Iterative algorithm for the split equality problem in Hilbert spaces

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Godwin Chidi Ugwunnadi
Keyword(s):  
Strong Convergence ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Split Equality Problem ◽  
Equality Problem

AbstractIn this paper, we studied the split equality problems (SEP) with a new proposed iterative algorithm and established the strong convergence of the proposed algorithm to solution of the split equality problems (SEP).

scholarly journals Design of Cascaded CNN for Medical Image Super Resolution

2021 ◽  
Vol 7 (3) ◽  
pp. 22-29
Author(s):  
Kajol Singh ◽  
Manish Saxena
Keyword(s):  
Neural Networks ◽  
Medical Image ◽  
Research Work ◽  
Super Resolution ◽  
Primary Objective ◽  
Lighting Conditions ◽  
Proposed Model ◽  
Filter Size ◽  
Medical Image Reconstruction ◽  
Image Super Resolution

The images captured through a camera usually belong to over or under exposed conditions. The reason may be inappropriate lighting conditions or camera resolution. Hence, it is of utmost importance to have a few enhancement techniques that could make these artefacts look better. Hence, the primary objective pertaining to the adjustment and enhancement techniques is to enhance the characteristics of an image. The initial numeric values related to an image get distorted when an image is enhanced. Therefore, enhancement techniques should be designed in such a way that the image quality isn’t compromised. This research work is focused on proposed a network design for deep convolution neural networks for application of super resolution techniques. To improve the complexity of existing techniques this work is intended towards network designs, different filter size and CNN architecture. The CNN model is most effective model for detection and segmentation in image. This model will improve the efficiency of medical image reconstruction from LR to HR. The proposed model showed its efficiency not only PET medical images but also on retinal database and achieved advance results as compared to existing works.

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