• Current Optics and Photonics
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• 제8권2호
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• pp.183-191
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• 2024

High-resolution retinal imaging based on adaptive optics (AO) is important for early diagnosis related to retinal diseases. However, in practical applications, closed-loop AO correction takes a relatively long time, and traditional open-loop correction methods have low accuracy in correction, leading to unsatisfactory imaging results. In this paper, a SH-U-net-based open-loop AO wavefront correction method is presented for a retinal AO imaging system. The SH-U-net builds a mathematical model of the entire AO system through data training, and the Root mean square (RMS) of the distorted wavefront is 0.08λ after correction in the simulation. Furthermore, it has been validated in experiments. The method improves the accuracy of wavefront correction and shortens the correction time.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2023년도 학술발표회
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• pp.161-161
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• 2023

Bias correction of values is a necessary step in downscaling coarse and systematically biased global climate models for use in local climate change impact studies. In addition to univariate bias correction methods, many multivariate methods which correct multiple variables jointly - each with their own mathematical designs - have been developed recently. While some literature have focused on the inter-comparison of these multivariate bias correction methods, none have focused extensively on the effect of diverse configurations (i.e., different combinations of input variables to be corrected) of climate variables, particularly high-dimensional ones, on the ability of the different methods to remove biases in uni- and multivariate statistics. This study evaluates the impact of three configurations (inter-variable, inter-spatial, and full dimensional dependence configurations) on four state-of-the-art multivariate bias correction methods in a national-scale domain over South Korea using a gridded approach. An inter-comparison framework evaluating the performance of the different combinations of configurations and bias correction methods in adjusting various climate variable statistics was created. Precipitation, maximum, and minimum temperatures were corrected across 306 high-resolution (0.2°) grid cells and were evaluated. Results show improvements in most methods in correcting various statistics when implementing high-dimensional configurations. However, some instabilities were observed, likely tied to the mathematical designs of the methods, informing that some multivariate bias correction methods are incompatible with high-dimensional configurations highlighting the potential for further improvements in the field, as well as the importance of proper selection of the correction method specific to the needs of the user.

• 한국수학교육학회지시리즈A:수학교육
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• 제49권2호
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• pp.161-174
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• 2010

The purpose of the study is to analyze various types of errors appeared in true-false proof problems of matrix and to find out correction method. In order to achieve this purpose, error test was conducted to the subject of 87 second grade students who were chosen from D high schoool. It was shown from this test that the most frequent error type was caused by the lack of understanding about concepts and essential facts of matrix(35.3%), and then caused by the invalid logically reasoning (27.4%), and then caused by the misusing conditions(18.7%). Through three hours of correction lessons with 5 students, the following correction teaching method was proposed. First, it is stressed that the operation rules and properties satisfied in real number system can not be applied in matrix. Second, it is taught that the analytical proof method and the reductio ad absurdum method are useful in the proof problem of matrix. Third, it is explained that the counter example of E=$\begin{pmatrix}1\;0\\0\;1 \end{pmatrix}$, -E should be found in proof of the false statement. Fourth, it is taught that the determinant condition should be checked for the existence of the inverse matrix.

• 대한수학회보
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• 제47권6호
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• pp.1329-1329
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• 2010

• 충청수학회지
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• 제27권3호
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• pp.403-404
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• 2014

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.307-321
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• 2004

In this paper, the unsteady Stokes problem is considered and also the pressure-correction method for the problem is described. At a fixed time level, we reduce the problem to two symmetric positive definite problems which depend on a time step parameter. Linear systems that arise from the problems are large, sparse, symmetric, positive definite and ill-conditioned as the time step tends to zero. Preconditioned problems based on an additive Schwarz method for solving the symmetric positive definite problems are derived and preconditioners are defined implicitly. It will be shown that the rate of convergence is independent of the mesh parameters as well as the time step size.

• 한국수자원학회논문집
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• 제54권7호
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• pp.475-484
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• 2021

상수관망의 최적설계는 절점의 최소 요구 수압을 만족함뿐만 아니라 관로비용의 최소화 등을 목적으로 한다. 상수관망 설계안의 수는 다양한 관의 배치로 인해 기하급수적으로 증가한다. 상수관망 설계에서 최적화된 설계를 제안하기 위해 다양한 최적화 알고리즘들이 적용되었다. 본 연구에서는 상수관망 최적설계에 자가적응형 매개변수를 개선한 Modified Hybrid Vision Correction Algorithm (MHVCA)을 적용하였다. 기존 Hybrid Vision Correction Algorithm (HVCA)의 Hybrid Rate (HR)를 비선형적 HR로 수정하여 성능을 개선하였다. 제안된 MHVCA의 성능을 확인하기 위해 결정변수가 2개 및 30개로 구성된 수학문제와 제약조건이 있는 수학문제에 적용하였다. MHVCA의 적용결과를 검토하기 위해 Harmony Search (HS), Improved Harmony Search (IHS), Vision Correction Algorithm (VCA) 및 HVCA와 비교하였다. 최종적으로 MHVCA를 상수관망 최적설계 문제에 적용하여 결과를 다른 알고리즘들과 비교하였다. 수학문제 및 상수관망 설계 문제에서 MHVCA가 다른 알고리즘들에 비해 좋은 결과를 보여주었다. MHVCA는 본 연구에서 적용한 문제뿐만 아니라 다양한 수자원공학 문제에 적용하여 좋은 결과를 보여줄 수 있을 것이다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권2호
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• pp.157-166
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• 2014

If there are metals located in the X-ray scanned object, a point outside the metals has its range of projection angle at which projections passing through the point are disturbed by the metals. Roughly speaking, this implies that attenuation information at the point is missing in the blocked projection range. So conventional projection completion MAR algorithms to use the undisturbed projection data on the boundary of the metaltrace is less efficient in reconstructing the attenuation coefficient in detailed parts, in particular, near the metal region. In order to overcome this problem, we propose the algebraic correction technique (ACT) to utilize a pre-reconstructed interim image of the attenuation coefficient outside the metal region which is obtained by solving a linear system designed to reduce computational costs. The reconstructed interim image of the attenuation coefficient is used as prior information for MAR. Numerical simulations support that the proposed correction technique shows better performance than conventional inpainting techniques such as the total variation and the harmonic inpainting.

• 한국산학기술학회논문지
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• 제20권6호
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• pp.314-321
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• 2019

본 연구에서 개발된 Self-Adaptive Vision Correction Algorithm (SAVCA)은 광학적 특성을 모방하여 개발된 Vision Correction Algorithm (VCA)의 총 6개의 매개변수 중 자가 적응형태로 구축된 Division Rate 1 (DR1) 및 Division Rate 2 (DR2)를 제외한 Modulation Transfer Function Rate (MR), Astigmatic Rate (AR), Astigmatic Factor (AF) 및 Compression Factor (CF) 등 4개의 매개변수를 변경하여 사용성을 증대시키기 위해 제시되었다. 개발된 SAVCA의 검증을 위해 기존 VCA를 적용하였던 2개 변수를 갖는 수학 문제 (Six hump camel back 및 Easton and fenton) 및 30개 변수를 갖는 수학 문제 (Schwefel 및 Hyper sphere)에 적용한 결과 SAVCA는 비교한 다른 알고리즘 (Harmony Search, Water Cycle Algorithm, VCA, Genetic Algorithms with Floating-point representation, Shuffled Complex Evolution algorithm 및 Modified Shuffled Complex Evolution)에 비해 우수한 성능을 보여주었다. 마지막으로 공학 문제인 Speed reducer design에서도 SAVCA는 가장 좋은 결과를 보여주었다. 복잡한 매개변수 조절과정을 거치지 않은 SAVCA는 여러 분야에서 적용이 가능할 것이다.

• 대한수학회보
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• 제50권6호
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• pp.1841-1846
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• 2013

In this paper we establish some new results on sums of Hilbert space frames and Riesz bases. We also provide a correction to some recently established results in [2].