• 대한수학회논문집
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• 제17권2호
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• pp.349-361
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• 2002

The ill-posed elliptic wave propagation problems can be transformed into well-posed initial value problems of the reflection and transmission operators characterizing the material structure of the given model by the combination of wave field splitting and invariant imbedding methods. In general, the derived scattering operator equations are of first-order in range, nonlinear, nonlocal, and stiff and oscillatory with a subtle fixed and movable singularity structure. The phase space and path integral analysis reveals that construction and reconstruction algorithms depend crucially on a detailed symbol analysis of the scattering operators. Some information about the singularity structure of the scattering operator symbols is presented and analyzed in the transversely homogeneous limit.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2002년도 ICCAS
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• pp.41.2-41
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• 2002

The stereo correspondence of two retinal images is one of the most difficult problems in stereo vision because the reconstruction of 3-D scene is a typical visual ill-posed problem. So far there still have been many unsolved problems, one of which is to reconstruct 3-D scene for a monochromatic surface because there is no clue to make a correspondence between two retinal images. We consider this problem with two layered self-organization neural network to simulate the competitive and cooperative interaction of binocular neurons. A...

• 충청수학회지
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• 제30권1호
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• pp.117-128
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• 2017

As an efficient way to determine the regularization parameter in the discrete ill-posed problems with multiple right-hand sides, we suggest global L-curve criterion as an extension of L-curve technique for image restoration problems with single right-hand side.

• 대한수학회논문집
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• 제33권3호
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• pp.1025-1037
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• 2018

We consider an ill-posed problem for the heat equation $u_{xx}=u_t$ in the quarter plane {x > 0, t > 0}. We propose a new method to compute the heat flux $h(t)=u_x(1,t)$ from the boundary temperature g(t) = u(1, t). The operator $g{\mapsto}h=Hg$ is unbounded in $L^2({\mathbb{R}})$, so we approximate h(t) by $h_{\delta}(t)=u_x(1+{\delta},\;t)$, ${\delta}{\rightarrow}0$. When noise is present, the data is $g_{\epsilon}$ leading to a corresponding heat $h_{{\delta},{\epsilon}}$. We obtain an estimate of the error ${\parallel}h-h_{{\delta},{\epsilon}}{\parallel}$, as well as the error when $h_{{\delta},{\epsilon}}$ is approximated by the trapezoidal rule. With an a priori choice rule ${\delta}={\delta}({\epsilon})$ and ${\tau}={\tau}({\epsilon})$, the step size of the trapezoidal rule, the main theorem gives the error of the heat flux as a function of noise level ${\epsilon}$. Numerical examples show that the proposed method is effective and stable.

• Structural Monitoring and Maintenance
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• 제3권2호
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• pp.115-127
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• 2016

It is a challenging problem of assessing the location and extent of structural damages with vibration measurements. In this paper, an improved Extended Kalman filter (EKF) with Tikhonov regularization is proposed to identify structural damages. The state vector of EKF consists of the initial values of modal coordinates and damage parameters of structural elements, therefore the recursive formulas of EKF are simplified and modal truncation technique can be used to reduce the dimension of the state vector. Then Tikhonov regularization is introduced into EKF to restrain the effect of the measurement noise for improving the solution of ill-posed inverse problems. Numerical simulations of a seven-story shear-beam structure and a simply-supported beam show that the proposed method has good robustness and can identify the single or multiple damages accurately with the unknown initial structural state.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.29-40
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• 2000

We provide semilocal convergence theorems for Newton-like methods in Banach space using outer and generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Frechet-derivative. This way our Newton-Kantorovich hypotheses differ from earlier ones. Our results can be used to solve undetermined systems, nonlinear least square problems and ill-posed nonlinear operator equations.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 1998년도 학술대회
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• pp.33-36
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• 1998

Most image restoration problems are ill-posed and need to e regularized. A difficult task in image regularization is to avoid smoothing of image edges. In this paper, were proposed an edge-preserving image restoration algorithm using block-based edge classification. In order to exploit the local image characteristics, we classify image blocks into edge and no-edge blocks. We then apply an adaptive constrained least squares (CLS) algorithm to eliminate noise around the edges. Experimental results demonstrate that the proposed algorithm can preserve image edges during the regularization process.

• 대한전자공학회논문지
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• 제25권12호
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• pp.1532-1540
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• 1988

Shape from shading problem, such as other most early visions, is ill-posed problems, which can be solved by the use of regularization methods. This paper proposes the three kinds of stabilizer for the regularization. These are integrability constraints and spline functionals. Parallel iterative schemes are derived in the form of the finite difference approximation. Experimental results, show that the average error in surface orientation is less than 5%.

• 대한전자공학회논문지
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• 제25권10호
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• pp.1141-1149
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• 1988

공간영역에서 모멘트방법을 써서 2차원 유전체의 복소 유전율 분포를 재구성 하기 위해 개발된 역산란 방법을 파수영역에서 사용할 수 있도록 개선하였다. 이 역산란 방법은 개념적으로 간단하고, 역산란 문제에 내재한 ill-posedness을 해결할 수 있는 여러 가지 적절한 방안을 강구할 수 있도록 한다.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.869-881
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• 2020

Most first kind integral equations are ill-posed, and obtaining their numerical solution often requires solving a linear system of algebraic equations of large condition number, which may be difficult or impossible. This article proposes a regularization-direct method to numerically solve first kind Fredholm integral equations. The vector forms of block-pulse functions and related properties are applied to formulate the direct method and reduce the integral equation to a linear system of algebraic equations. We include a regularization scheme to overcome the ill-posedness of integral equation and obtain a stable numerical solution. Some test problems are solved using the proposed regularization-direct method to illustrate its efficiency for solving first kind Fredholm integral equations.