• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1209-1220
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• 2014

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder$\acute{o}$n-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

• ETRI Journal
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• v.35 no.5
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• pp.923-926
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• 2013

To resolve video enhancement problems, a novel method of gradient domain fusion wherein gradient domain frames of the background in daytime video are fused with nighttime video frames is proposed. To verify the superiority of the proposed method, it is compared to conventional techniques. The implemented output of our method is shown to offer enhanced visual quality.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.75-87
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• 2002

The shape derivative for the domain functional will be discussed in the situation of domain inclusion. Hadamard's shape structure is sought by using the material derivative in conjunction with the domain imbedding technique.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.9
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• pp.3745-3761
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• 2020

Low-rank representation methods already achieve many applications in the image reconstruction. However, for high-gradient image patches with rich texture details and strong edge information, it is difficult to find sufficient similar patches. Existing low-rank representation methods usually destroy image critical details and fail to preserve edge structure. In order to promote the performance, a new representation-based image super-resolution reconstruction method is proposed, which combines gradient domain guided image filter with the structure-constrained low-rank representation so as to enhance image details as well as reveal the intrinsic structure of an input image. Firstly, we extract the gradient domain guided filter of each atom in high resolution dictionary in order to acquire high-frequency prior information. Secondly, this prior information is taken as a structure constraint and introduced into the low-rank representation framework to develop a new model so as to maintain the edges of reconstructed image. Thirdly, the approximate optimal solution of the model is solved through alternating direction method of multipliers. After that, experiments are performed and results show that the proposed algorithm has higher performances than conventional state-of-the-art algorithms in both quantitative and qualitative aspects.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.49 no.4
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• pp.32-39
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• 2012

This paper develops a robust image enhancement method by adjusting image signal energy according to the direction and the variation of image signal in DCT domain. To accomplish this, we measure the gradient of image signal directly in DCT domain and then adjust frequency components involved in sharpness, local contrast and global contrast using the direction and the magnitude of the measured gradient The experiment showed that the proposed method produces the best quality of an image without causing blocking, ringing artifacts and boosting noise.

• The Journal of the Acoustical Society of Korea
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• v.24 no.2E
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• pp.54-60
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• 2005

A new multichannel blind deconvolution algorithm is proposed for speech mixtures. It employs unidirectional filters and normalization of gradient terms in the frequency domain. The proposed algorithm is shown to be approximately nonholonomic. Thus it provides improved convergence and separation performances without whitening effect for nonstationary sources such as speech and audio signals. Simulations using real world recordings confirm superior performances over existing algorithms and its usefulness for real applications.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.1
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• pp.72-79
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• 1997

Most open magnetic resonance imaging systems have used the planar gradient coils whose inductances were minimized through the magnetic energy minimization procedure in the spatial frequency domain. Though the planar gradient coils have smaller inductance than conventional gradient coils, the planar gradient coils often suffer from their poor magnetic field linearity. Scaling the spatial frequencies of the current density function designed by the magnetic energy minimization, magnetic field linearity of the planar gradient coils can be greatly improved with small sacrifice of gradient coil inductance. We have found that the figure of merit of the planar gradient coils, defined by the gradient strength divided by the linearity error and the inductance, can be improved by proposed technique.

• Journal of Sensor Science and Technology
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• v.16 no.3
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• pp.202-210
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• 2007

The aim of this study is to acquire useful information of lower urinary tract symptom (LUTS) diagnosis through urophonography signal as a noninvasive method. The hardware and software which could evaluate the function of compensatory hypertrophy with noninvasive and comfortable method was implemented to measure uroflow and urophonography signal during urination. The PSD (power spectrum density) and the log-log plot gradient analysis were accomplished in frequency domain. For evaluation of the system and analysis method, a model system for the lower urinary system of men was used. From the evaluation of the model system, the PDS and the log-log plot gradient were dependent on the occlusion degree significantly. In a pilot study on normal and abnormal male subjects, the PSD and the log-log plot gradient were highly correlated with the artificial urethral obstruction.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2011.11a
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• pp.331-332
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• 2011

본 논문에서는 Markov random field (MRF) 프레임워크와 영상의 기울기(gradient) 정보를 이용한 필드영상의 공간적 디인터레이싱(deinterlacing) 알고리즘을 제안한다. 기존의 디인터레이싱 결과를 보면 때때로 에지 부분의 연결이 정밀하지 못하여 눈에 거슬리는 재깅(jagging) 현상 등의 결함이 나타나기도 하는데, 제안하는 알고리즘은 이러한 현상을 줄이고자 영상의 기울기 도메인(gradient domain)에서 디인터레이싱을 수행한다. 즉, 제안하는 방식은 필드 영상으로부터 기울기 영상을 얻고 이를 보간한 후 필드영상과 복원된 기울기 영상을 토대로 원본 영상을 복원한다. 이 과정에서 각각의 픽셀마다 기울기 영상의 보간을 위한 에지 방향의 추정이 필요한데, 이 과정에서는 MRF 모델을 기반으로 에너지 함수를 설계하고 최적화시킴으로써 보다 강건한 추정결과를 얻도록 하였다. 프레임 영상 복원은 기울기 영상과 필드 영상 정보를 사전 정보로 하여 선형 방정식을 세우고 푸는 과정으로 이루어진다. 실험한 결과, 제안된 방법의 결과가 기존 방법에 비하여 눈에 띄는 결함을 줄이고 좋은 성능을 보임을 확인할 수 있다.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.585-594
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• 2022

In this article we classify four dimensional gradient Ricci solitons (M, g, f) with half harmonic Weyl curvature and at most two distinct Ricci-eigenvalues at each point. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, (V, g) is isometric to one of the following: (i) an Einstein manifold. (ii) a domain in the Riemannian product (ℝ², g₀) × (N, ${\tilde{g}}$), where g₀ is the flat metric on ℝ² and (N, ${\tilde{g}}$) is a two dimensional Riemannian manifold of constant curvature λ ≠ 0. (iii) a domain in ℝ × W with the warped product metric $ds^2+h(s)^2{\tilde{g}}$, where ${\tilde{g}}$ is a constant curved metric on a three dimensional manifold W.