• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.285-301
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• 2022

In this paper, we mainly study the random sampling and reconstruction of signals living in the subspace V^p(𝚽, 𝚲) of L^p(ℝ^d), which is generated by a family of molecules 𝚽 located on a relatively separated subset 𝚲 ⊂ ℝ^d. The space V^p(𝚽, 𝚲) is used to model signals with finite rate of innovation, such as stream of pulses in GPS applications, cellular radio and ultra wide-band communication. The sampling set is independently and randomly drawn from a general probability distribution over ℝ^d. Under some proper conditions for the generators 𝚽 = {𝜙_λ : λ ∈ 𝚲} and the probability density function 𝜌, we first approximate V^p(𝚽, 𝚲) by a finite dimensional subspace V^p_N (𝚽, 𝚲) on any bounded domains. Then, we prove that the random sampling stability holds with high probability for all signals in V^p(𝚽, 𝚲) whose energy concentrate on a cube when the sampling size is large enough. Finally, a reconstruction algorithm based on random samples is given for signals in V^p_N (𝚽, 𝚲).

• Wind and Structures
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• v.38 no.4
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• pp.231-244
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• 2024

As wind farms expand into low wind speed areas, an increasing number are being established in mountainous regions. To fully utilize wind energy resources, it is essential to understand the details of mountain flow fields. Reconstructing the wind speed field in complex terrain is crucial for planning, designing, operation of wind farms, which impacts the wind farm's profits throughout its life cycle. Currently, wind speed reconstruction is primarily achieved through physical and machine learning methods. However, physical methods often require significant computational costs. Therefore, we propose a Full Convolutional Neural Network (FCNN)-based reconstruction method for mountain wind velocity fields to evaluate wind resources more accurately and efficiently. This method establishes the mapping relation between terrain, wind angle, height, and corresponding velocity fields of three velocity components within a specific terrain range. Guided by this mapping relation, wind velocity fields of three components at different terrains, wind angles, and heights can be generated. The effectiveness of this method was demonstrated by reconstructing the wind speed field of complex terrain in Beijing.

• Proceedings of the Optical Society of Korea Conference
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• 2008.02a
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• pp.113-114
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• 2008

• Proceedings of the Optical Society of Korea Conference
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• 2008.02a
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• pp.191-192
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• 2008

• The Bulletin of The Korean Astronomical Society
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• v.40 no.1
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• pp.67.1-67.1
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• 2015

In the past two decades, diverse methods and computer codes for reconstruction of coronal magnetic fields have been developed. Some of them can reproduce a known analytic solution quite well when the magnetic field vector is fully specified by the known solution at the domain boundaries. In practical problems, however, we do not know the boundary conditions in the computational domain except the photospheric boundary, where vector magnetogram data are provided. We have developed a new, simple variational method employing vector potentials. We have tested the computational code based on this method for problems with known solutions and those with actual photospheric data. When solutions are fully given at all boundaries, the accuracy of our method is almost comparable to best performing methods in the market. When magnetic field vectors are only given at the photospheric boundary, our method excels other methods in "figures of merit" devised by Schrijver et al. (2006). Our method is expected to contribute to the real time monitoring of the sun required for future space weather prediction.

• Journal of the Optical Society of Korea
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• v.19 no.4
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• pp.390-396
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• 2015

We propose a partial occlusion removal method for computational integral imaging reconstruction (CIIR) based on the usage of the exemplar based inpainting technique. The proposed method is an improved version of the original linear inpainting based CIIR (LI-CIIR), which uses the inpainting technique to fill in the data missing region. The LI-CIIR shows good results for images which contain objects with smooth surfaces. However, if the object has a textured surface, the result of the LI-CIIR deteriorates, since the linear inpainting cannot recover the textured data in the data missing region well. In this work, we utilize the exemplar based inpainting to fill in the textured data in the data missing region. We call the proposed method the neighboring elemental image exemplar based inpainting (NEI-exemplar inpainting) method, since it uses sources from neighboring elemental images to fill in the data missing region. Furthermore, we also propose an automatic occluding region extraction method based on the use of the mutual constraint using depth estimation (MC-DE) and the level set based bimodal segmentation. Experimental results show the validity of the proposed system.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.14 no.11
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• pp.2563-2568
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• 2010

SAII (synthetic aperture integral imaging) is a useful technique to record many multi view images of 3D objects by using a moving camera and to reconstruct 3D depth images from the recorded multiviews. This is largely composed of two processes. A pickup process provides elemental images of 3D objects and a reconstruction process generates 3D depth images computationally. In this paper, a signal model for SAII is presented. We defined the granular noise and analyzed its characteristics. Our signal model revealed that we could reduce the noise in the reconstructed images and increase the computational speed by reducing the shifting distance of a single camera.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.2
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• pp.87-93
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• 2007

Generally, the analysis using Computational Fluid Dynamics(CFD) is necessary for aircraft design. However, the analysis using CFD, it requires a lot of computational time and cost. But we can reduce grid reconstruction time of analyzing the various models if we use dynamic mesh. In addition, dynamic mesh can be an efficient technique in aeroelastic analysis and design optimization problem because these problems need grid reconstruction process frequently.

• Journal of Computational Design and Engineering
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• v.2 no.4
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• pp.261-267
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• 2015

Free-form blades are widely used in different industries, such as aero-engine and steam turbine. Blades that are damaged during service or have production deficiencies are usually replaced with new ones. This leads to the waste of expensive material and is not sustainable. However, material and costs can be saved by repairing of locally damaged blades or blades with localized production deficiencies. The blade needs to be further machined after welding process to reach the aerodynamic performance requirements. This paper outlines an adaptive location approach of repaired blade for model reconstruction and NC machining. Firstly, a mathematical model is established to describe the localization problem under constraints. Secondly, by solving the mathematical model, localization of repaired blade for NC machining can be obtained. Furthermore, a more flexible method based on the proposed mathematical model and the continuity of the deformation process is developed to realize a better localization. Thirdly, by rebuilding the model of the repaired blade and extracting repair error, optimized tool paths for NC machining is generated adaptively for each individual part. Finally, three examples are given to validate the proposed method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.4
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• pp.301-327
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• 2019

The proper orthogonal decomposition (POD) method for time-dependent problems significantly reduces the computational time as it reduces the original problem to the lower dimensional space. Even a higher degree of reduction can be reached if the solution is smooth in space and time. However, if the solution is discontinuous and the discontinuity is parameterized e.g. with time, the POD approximations are not accurate in the reduced space due to the lack of ability to represent the discontinuous solution as a finite linear combination of smooth bases. In this paper, we propose to post-process the sample solutions and re-initialize the POD approximations to deal with discontinuous solutions and provide accurate approximations while the computational time is reduced. For the post-processing, we use the Gegenbauer reconstruction method. Then we regularize the Gegenbauer reconstruction for the construction of POD bases. With the constructed POD bases, we solve the given PDE in the reduced space. For the POD approximation, we re-initialize the POD solution so that the post-processed sample solution is used as the initial condition at each sampling time. As a proof-of-concept, we solve both one-dimensional linear and nonlinear hyperbolic problems. The numerical results show that the proposed method is efficient and accurate.