• Kyungpook Mathematical Journal
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• 제64권2호
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• pp.353-369
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• 2024

In this study, we investigate the unknown time-dependent heat source function in inverse problems. We consider three general nonlocal conditions; two classical boundary conditions and one nonlocal over-determination, condition, these genereate six different cases. The finite integration method (FIM), based on numerical integration, has been adapted to solve PDEs, and we use it to discretize the spatial domain; we use backward differences for the time variable. Since the inverse problem is ill-posed with instability, we apply regularization to reduce the instability. We use the first-order Tikhonov's regularization together with the minimization process to solve the inverse source problem. Test examples in all six cases are presented in order to illustrate the accuracy and stability of the numerical solutions.

• 한국측량학회지
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• 제20권2호
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• pp.155-164
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• 2002

본 연구에서는 상업용 고해상도 위성인 IKONOS 위성 영상의 기하보정 방법에 대해 알아보기 위해 기존에 쓰여왔던 다항식모델과 위성의 보조데이터 없이 기하보정이 가능한 RM을 적용하여 각각의 차수와 기준점의 수에 따른 정확도를 비교 분석하였다. 또한 RFM 계수산출을 위한 최소제곱법의 수치적 불안정성을 극복하기 위하여 Tikhonov 정규화기법을 도입하여 적용하였다. RFM 적응 결과, 기존의 2차원 다항식 모델에 비해 평균제곱근오차를 2 pixel 이상 감소시킬 수 있었다.

• 대한기계학회논문집B
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• 제28권10호
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• pp.1271-1278
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• 2004

In order to measure non-intrusively velocity profile in liquid metal flow, a modified electromagnetic flowmeter was designed, which was based on electromagnetic tomography technique. Under the assumption that flow is fully-developed, axisymmetric and rectilinear, the velocity profile was reconstructed after the flowmeter equation, the first kind of Fredholm integration equation, was linearized. In reconstruction process Tikhonov regularization method with regularization parameter was used. The reconstructed velocity profile had the nearly same as turbulent flow profile which was approximately represented as log law. In addition, flowmeter output fur a fixed magnet rotation angle was linearly proportional to flow rate. When magnet rotation angle was 54$^{\circ}$, axisymmetric weight function was nearly uniform so that the flowmeter gives a constant signal for any fully-developed, axisymmetric and rectilinear profile with a constant flow rate.

• 대한수학회지
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• 제54권2호
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• pp.613-626
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• 2017

For the overdetermined linear system, when both the data matrix and the observed data are contaminated by noise, Total Least Squares method is an appropriate approach. Since an ill-conditioned data matrix with noise causes a large perturbation in the solution, some kind of regularization technique is required to filter out such noise. In this paper, we consider a Dual regularized Total Least Squares problem. Unlike the Tikhonov regularization which constrains the size of the solution, a Dual regularized Total Least Squares problem considers two constraints; one constrains the size of the error in the data matrix, the other constrains the size of the error in the observed data. Our method derives two nonlinear equations to construct the iterative method. However, since the Jacobian matrix of two nonlinear equations is not guaranteed to be nonsingular, we adopt a trust-region based iteration method to obtain the solution.

• Communications for Statistical Applications and Methods
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• 제23권1호
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• pp.71-83
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• 2016

In this paper we discuss a deconvolution density estimator obtained using the support vector machines (SVM) and Tikhonov's regularization method solving ill-posed problems in reproducing kernel Hilbert space (RKHS). A remarkable property of SVM is that the SVM leads to sparse solutions, but the support vector deconvolution density estimator does not preserve sparsity as well as we expected. Thus, in section 3, we propose another support vector deconvolution estimator (method II) which leads to a very sparse solution. The performance of the deconvolution density estimators based on the support vector method is compared with the classical kernel deconvolution density estimator for important cases of Gaussian and Laplacian measurement error by means of a simulation study. In the case of Gaussian error, the proposed support vector deconvolution estimator shows the same performance as the classical kernel deconvolution density estimator.

• 대한전자공학회논문지
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• 제27권6호
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• pp.972-981
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• 1990

Many researchers have been interested in whether complex computational problems can be solved by the neural net or not. Especially, problems of early vision are integrated by Tikhonov's regularization theory. Regularization technique can be realized in resistive net. In this paper, we suggest the resistive net with upper and lower thresholder to be able to compute shape from shading and to solve its discontinuous problem. We simulate three algorithms-Horn's algorithm, resistive net and up-low thrwsholding net -with respect to three cases-fully boundary, boundary losing partly and noisy image. As being able to cope with crease and discontinuous parts, we get the good 3D shape from shading.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.1749-1754
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• 2004

In order to measure non-intrusively velocity profile in liquid metal flow, a modified electromagnetic flowmeter was designed, which was based on electromagnetic tomography technique. Under the assumption that flow is fully-developed, axisymmetric and rectilinear, the velocity profile was reconstructed after the flowmeter equation, the first kind of Fredholm integration equation, was linearized. In reconstruction process Tikhonov regularization method with regularization parameter was used. The reconstructed velocity profile had the nearly same as turbulent flow profile which was approximately represented as log law. In addition, flowmeter output for a fixed magnet rotation angle was linearly proportional to flow rate. When magnet rotation angle was $54^{\circ}$, axisymmetric weight function was nearly uniform so that the flowmeter gives a constant signal for any fully-developed, axisymmetric and rectilinear profile with a constant flow rate.

• 충청수학회지
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• 제22권2호
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• pp.177-186
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• 2009

The global least squares method (Gl-LSQR) is a generalization of LSQR method for solving linear system with multiple right hand sides. In this paper, we present how to apply this algorithm for solving the image restoration problem and illustrate the usefulness and effectiveness of this method from numerical experiments.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.531-540
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• 2018

We first show how to construct the linear operator equations corresponding to Tikhonov regularization problems for solving image deblurring problems with nearly separable point spread functions. We next propose a Kronecker product preconditioner which is suitable for the global PCG method. Lastly, we provide numerical experiments of the global PCG method with the Kronecker product preconditioner for several image deblurring problems to evaluate its effectiveness.

• 충청수학회지
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• 제24권4호
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• pp.895-903
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• 2011

A two dimensional version of LSQR iterative algorithm which takes advantages of working solely with the 2-dimensional arrays is developed and applied to the image deblurring problem. The efficiency of the method comparing to the Fourier-based LSQR method and the 2-D version CGLS algorithm methods proposed by Hanson ([4]) is analyzed.