• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2019.06a
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• pp.98-101
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• 2019

At present, deep convolutional neural networks have made a very important contribution in single-image super-resolution. Through the learning of the neural networks, the features of input images are transformed and combined to establish a nonlinear mapping of low-resolution images to high-resolution images. Some previous methods are difficult to train and take up a lot of memory. In this paper, we proposed a simple and compact deep recursive residual network learning the features for single image super resolution. Global residual learning and local residual learning are used to reduce the problems of training deep neural networks. And the recursive structure controls the number of parameters to save memory. Experimental results show that the proposed method improved image qualities that occur in previous methods.

• Journal of the Semiconductor & Display Technology
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• v.18 no.1
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• pp.102-104
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• 2019

Registering different kinds of clinical images widely used in diagnostic and surgery planning. However, cause of tumor growth or effected by gravity, human tissue has plenty of non-rigid deformation with clinically. Non-rigid registration allows the mapping of straight lines to curves. Therefore, such local deformation makes registration more complicated. In this work, we mainly introduce intra-subject, inter-modality registration. This paper mainly studies the nonlinear registration method of 2D medical image registration. The general medical image registration algorithm requires manual intervention, and cost long registration time. In our work to reduce the registration time in rough registration step, the barycenter and the direction of main axis of the image is calculated, which reduces the calculation amount compared with the method of using mutual information.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2018.06a
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• pp.63-66
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• 2018

Recently, a convolutional neural network (CNN) models at single image super-resolution have been very successful. Residual learning improves training stability and network performance in CNN. In this paper, we compare four convolutional neural network models for super-resolution (SR) to learn nonlinear mapping from low-resolution (LR) input image to high-resolution (HR) target image. Four models include general CNN model, global residual learning CNN model, local residual learning CNN model, and the CNN model with global and local residual learning. Experiment results show that the results are greatly affected by how skip connections are connected at the basic CNN network, and network trained with only global residual learning generates highest performance among four models at objective and subjective evaluations.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.433-442
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• 2021

Let X and X^* be a Banach space and its dual, respectively, and let B(X) and S(X) be the unit ball and unit sphere of X, respectively. In this paper, we study the relation between Modulus of n-dimensional U-convexity in X^* and normal structure in X. Some new results about fixed points of nonexpansive mapping are obtained, and some existing results are improved. Among other results, we proved: if X is a Banach space with $U^n_{X^*}(n+1)>1-{\frac{1}{n+1}}$ where n ∈ ℕ, then X has weak normal structure.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.203-221
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• 2022

In this paper, we introduce new hybrid inertial contraction projection algorithms for solving variational inequality problems over the intersection of the fixed point sets of demicontractive mappings in a real Hilbert space. The proposed algorithms are based on the hybrid steepest-descent method for variational inequality problems and the inertial techniques for finding fixed points of nonexpansive mappings. Strong convergence of the iterative algorithms is proved. Several fundamental experiments are provided to illustrate computational efficiency of the given algorithm and comparison with other known algorithms

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.451-474
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• 2021

In this paper, we investigate a hybrid algorithm for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators which is also a common fixed point problem for finite family of relatively quasi-nonexpansive mappings and split feasibility problem in uniformly convex real Banach spaces which are also uniformly smooth. The iterative algorithm employed in this paper is design in such a way that it does not require prior knowledge of operator norm. We prove a strong convergence result for approximating the solutions of the aforementioned problems and give applications of our main result to minimization problem and convexly constrained linear inverse problem.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.971-983
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• 2021

In this paper, we prove common fixed point theorems for six weakly compatible mappings in G-fuzzy metric spaces introduced by Sun and Yang [16] which is actually generalization of G-metric spaces. G-metric spaces coined by Mustafa and Sims [13]. The paper concerns our sustained efforts for the materialization of G-fuzzy metric spaces and their properties. We also exercise the concept of symmetric G-fuzzy metric space, 𝜙-function and weakly compatible mappings. The results present in this paper generalize the well-known comparable results in the literature. We justify our results by suitable examples. Some applications are also given in support of our results.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.1-22
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• 2022

The purpose of this research is to formulate a new proximal-type algorithm to solve the equilibrium problem in a real Hilbert space. A new algorithm is analogous to the famous two-step extragradient algorithm that was used to solve variational inequalities in the Hilbert spaces previously. The proposed iterative scheme uses a new step size rule based on local bifunction details instead of Lipschitz constants or any line search scheme. The strong convergence theorem for the proposed algorithm is well-proven by letting mild assumptions about the bifunction. Applications of these results are presented to solve the fixed point problems and the variational inequality problems. Finally, we discuss two test problems and computational performance is explicating to show the efficiency and effectiveness of the proposed algorithm.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.449-469
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• 2022

This paper deals with the new iterative algorithm for approximating the fixed point of generalized 𝛼-nonexpansive mappings in a hyperbolic space. We show that the proposed iterative algorithm is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur and Piri iteration processes for contractive mappings in a Banach space. We also establish some weak and strong convergence theorems for generalized 𝛼-nonexpansive mappings in hyperbolic space. The examples and numerical results are provided in this paper for supporting our main results.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.123-134
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• 2023

Since Knaster, Kuratowski, and Mazurkiewicz established their KKM theorem in 1929, it was first applied to topological vector spaces mainly by Fan and Granas. Later it was extended to convex spaces by Lassonde and to extensions of c-spaces by Horvath. In 1992, such study was called the KKM theory by ourselves. Then the theory was extended to generalized convex spaces or G-convex spaces. Motivated by such spaces, there have appeared several particular types of artificial spaces. In 2006 we introduced abstract convex spaces which contain all existing spaces appeared in the KKM theory. Later in 2014-2020, Khahn and Quan introduced "topologically based existence theorems" and the so-called KKM structure. In the present paper, we show that their structure is a particular type of already known KKM spaces.