• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.1715-1718
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• 2003

본 논문에서 우리는 정규화 된 혼합 노름(norm)을 이용한 다중 채널 영상 복원 알고리즘을 제안한다. 채널 내부와 채널 사이의 결정론적 정보를 이용하는 다중채널 복원 문제를 고려한다. 각 채널에서, LMS(Least Mean Square), LMF(Least Mean Fourth), 평탄 함수가 결합된 함수가 제안되었다. LMS와 LMF 사이의 적절한 분배를 제어하는 혼합 노를 매개변수와 해의 평탄 정도를 정의하는 정규화 매개 변수를 소개하며, 두 매개 변수는 각 채널의 잡음 특성에 따라 매번 반복적으로 갱신된다. 제안된 알고리즘은 각 채널의 잡음분포에 대한 지식이 필요하지 앉고 앞에서 언급된 매개 변수는 부분적으로 복원된 영상에 기반을 두고 조절하게 된다.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.267-285
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• 2014

An upstream scheme based on the pseudostress-velocity mixed formulation is studied to solve convection-dominated Oseen equations. Lagrange multipliers are introduced to treat the trace-free constraint and the lowest order Raviart-Thomas finite element space on rectangular mesh is used. Error analysis for several quantities of interest is given. Particularly, first-order convergence in $L^2$ norm for the velocity is proved. Finally, numerical experiments for various cases are presented to show the efficiency of this method.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.403-417
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• 2021

This note is devoted to establishing the boundedness for some classes of Littlewood-Paley square operators defined by the kernels without any regularity on the mixed radial-angular spaces. The corresponding vector-valued versions are also presented. As applications, the corresponding results for the Littlewood-Paley g∗λ function and the Littlewood-Paley function related to the area integrals are also obtained.

• Journal of the Korean Mathematical Society
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• v.28 no.1
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• pp.79-86
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• 1991

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.3
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• pp.163-168
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• 2000

The problems of mixed $H_2/H_{\infty}$ filtering design fer continuous and discrete time linear systems with time delay are investigated. The main purpose is to design a stable mixed $H_2/H_{\infty}$ filter which minimizes the H$_2$Performance measure satisfying a prescribed H$_{\infty}$ norm bound on the closed loop system in continuous-time case and discrete-time case, respectively. The sufficient conditions of existence of filter, the mixed $H_2/H_{\infty}$ filter design method, and the upper bound of performance measure are proposed by LMI(linear matrix inequality) techniques in terms of all finding variables. Also, we present optimization problems in order to get the optimal mixed $H_2/H_{\infty}$ filter in continuous and discrete time case, respectively.

• Communications of the Korean Mathematical Society
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• v.30 no.1
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• pp.23-34
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• 2015

We use mixed norm estimates for the spherical averaging operator to obtain some results concerning pinned distance sets.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.733-763
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• 2006

We study quasi-stationary Stokes flow in a dihedral domain arising from a study of a free boundary problem of viscous fluid in a container. We construct an exact solution of quasi-stationary Stokes equations and derive its estimates with norm in a weighted Sobolev spaces.

• Journal of Electrical Engineering and information Science
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• v.1 no.1
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• pp.29-38
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• 1996

To improve the reliability of control systems, certain robustness to plant uncertainties and disturbance inputs is required in terms of well founded mathematical basis. Robust control theory was set up and developed until now from this motivation. In this field, H$_2$or H\ulcorner norm performance measures are frequently used nowadays. Moreover a mixed H$_2$/H\ulcorner control problem is introduced to combine the merits of each measure since H$_2$control usually makes more sense for performance while H\ulcorner control is better for robustness to plant perturbations. However only some partial analytic solutions are developed to this problem under certain special cases at this time. In this paper, the mixed H$_2$/H\ulcorner control problem is considered. The analytic(or semi-analytic) solutions of (sub)optimal mixed H$_2$/H\ulcorner state-feedback controller are derived for the scalar plant case and the multivariable plant case, respectively. An illustrative example is given to compare the proposed analytic solution with the existing numerical one.

• Journal of IKEEE
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• v.25 no.1
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• pp.139-147
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• 2021

This paper introduces an image decomposition-based deep learning method and loss function to improve low-light images. In order to remove color distortion and halo artifact, illuminance channel of an input image is decomposed into reflectance and luminance channels, and a decomposition-based multiple structural deep learning process is applied to each channel. In addition, a mixed norm-based loss function is described to increase the stability and remove blurring in reconstructed image. Experimental results show that the proposed method effectively improve various low-light images.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1043-1057
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• 2000

This paper is devoted to the investigation of mixed Fourier-Bessel transformation (※Equations, See Full-text) We apply the method of [6] which provides the estimate for weighted L(sub)$\infty$-norm of the spherical mean of │f│$^2$ via its weighted L$_1$-norm (generally it is wrong without the requirement of the non-negativity of f). We prove that in the case of Fourier-Bessel transformatin the mentioned method provides (in dependence on the relation between the dimension of the space of non-special variables n and the length of multiindex ν) similar estimates for weighted spherical means of │f│$^2$, the allowed powers of weights are also defined by multiindex ν. Further those estimates are applied to partial differential equations with singular Bessel operators with respect to y$_1$, …, y(sub)m and we obtain the corresponding estimates for solutions of the mentioned equations.