• Current Optics and Photonics
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• v.5 no.3
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• pp.270-277
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• 2021

The adaptive sparse representation (ASR) can effectively combine the structure information of a sample dictionary and the sparsity of coding coefficients. This algorithm can effectively consider the correlation between training samples and convert between sparse representation-based classifier (SRC) and collaborative representation classification (CRC) under different training samples. Unlike SRC and CRC which use fixed norm constraints, ASR can adaptively adjust the constraints based on the correlation between different training samples, seeking a balance between l₁ and l₂ norm, greatly strengthening the robustness and adaptability of the classification algorithm. The correlation coefficients (CC) can better identify the pixels with strong correlation. Therefore, this article proposes a hyperspectral image classification method called correlation coefficients and adaptive sparse representation (CCASR), based on ASR and CC. This method is divided into three steps. In the first step, we determine the pixel to be measured and calculate the CC value between the pixel to be tested and various training samples. Then we represent the pixel using ASR and calculate the reconstruction error corresponding to each category. Finally, the target pixels are classified according to the reconstruction error and the CC value. In this article, a new hyperspectral image classification method is proposed by fusing CC and ASR. The method in this paper is verified through two sets of experimental data. In the hyperspectral image (Indian Pines), the overall accuracy of CCASR has reached 0.9596. In the hyperspectral images taken by HIS-300, the classification results show that the classification accuracy of the proposed method achieves 0.9354, which is better than other commonly used methods.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.9-22
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• 2002

We consider the hp-version to solve non-constant coefficient elliptic equations with Dirichlet boundary conditions on a bounded, convex polygonal domain $\Omega$ in $R^{2}.$ To compute the integrals in the variational formulation of the discrete problem we need the numerical quadrature rule scheme. In this paler we consider a family $G_{p}= {I_{m}}$ of numerical quadrature rules satisfying certain properties. When the numerical quadrature rules $I_{m}{\in}G_{p}$ are used for calculating the integrals in the stiffness matrix of the variational form we will give its variational fore and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_0,{\Omega}'$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.2
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• pp.125-140
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• 2010

This paper develops a least-squares approach to the solution of the optimal control problem for the Navier-Stokes equations. We recast the optimality system as a first-order system by introducing velocity-flux variables and associated curl and trace equations. We show that a least-squares principle based on $L^2$ norms applied to this system yields optimal discretization error estimates in the $H^1$ norm in each variable.

• Journal of Soil and Groundwater Environment
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• v.18 no.3
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• pp.82-92
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• 2013

This study has investigated naturally occurring radioactive materials (N.O.R.M; $^{238}U$, $^{222}Rn$) for 353 drinking groundwater wells in metamorphic rock areas in Korea. Uranium concentrations ranged from N.D (not detected) to 563.56 ${\mu}g/L$ (median value, 0.68 ${\mu}g/L$) and radon concentrations ranged from 108 to 11,612 pCi/L (median value, 1,400 pCi/L). Uranium and radon concentrations in the groundwater generally are similar to USA with similar geological setting. Uranium concentrations in 9 wells (2.6%) exceeded 30 ${\mu}g/L$, which is the maximum contaminant level (MCL) by the US environmental protection agency (EPA), radon concentrations in 46 wells (13%) exceeded 4,000 pCi/L, which is the Alternative MCL (AMCL) by the US.EPA. The log-log correlation coefficient between uranium and radon was 0.32. The correlation coefficient between uranium and pH was 0.12 and the correlation coefficient between radon and temperature was -0.01. The correlation coefficient between uranium and $HCO_3$ was 0.09 and the correlation coefficient between uranium and Ca was 0.11. The median value of uranium was high Chung-Buk (1.78 ${\mu}g/L$), Gyeong-Buk (1.37 ${\mu}g/L$), In-Cheon (1.06 ${\mu}g/L$) for each province. On the other hand, the median value of radon was high In-Cheon (2,962 pCi/L), Chung-Buk (2,339 pCi/L), Jeon-Buk (2,165 pCi/L) for each province. Jeon-Buk for log-log correlation coefficient is the highest (0.63) among provinces.

• Journal of Korean Institute of Industrial Engineers
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• v.32 no.2
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• pp.74-81
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• 2006

In this paper, we deal with the separation of data by concurrently determined, piecewise nonlinear discriminant functions. Toward the end, we develop a new $l_1$-distance norm error metric and cast the problem as a mixed 0-1 integer and linear programming (MILP) model. Given a finite number of discriminant functions as an input, the proposed model considers the synergy as well as the individual role of the functions involved and implements a simplest nonlinear decision surface that best separates the data on hand. Hence, exploiting powerful MILP solvers, the model efficiently analyzes any given data set for its piecewise nonlinear separability. The classification of four sets of artificial data demonstrates the aforementioned strength of the proposed model. Classification results on five machine learning benchmark databases prove that the data separation via the proposed MILP model is an effective supervised learning methodology that compares quite favorably to well-established learning methodologies.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.1
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• pp.32-39
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• 2002

Vector quantization for image compression needs expensive encoding time to find the closest codeword to the input vector. This paper proposes a search algorithm for fast vector quantization encoding. Firstly, we derive a robust condition based on the efficient topological structure of the codebook to dramatically eliminate unnecessary matching operations from the search procedure. Then, we Propose a fast search algorithm using the elimination condition. Simulation results show that with little preprocessing and memory cost, the encoding time of the proposed algorithm is reduced significantly while the encoding quality remains the same with respect to the full search algorithm. It is also found that the Proposed algorithm outperforms the existing search algorithms.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.211-236
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• 2019

This paper is devoted to the study and investigation of the Runge-Kutta discontinuous Galerkin method for a system of differential equations consisting of two hyperbolic conservation laws. The numerical coupling flux which is used at a given interface (x = 0) is the upwind flux. Moreover, in the linear case, we derive optimal convergence rates in the $L_2$-norm, showing an error estimate of order ${\mathcal{O}}(h^{k+1})$ in domains where the exact solution is smooth; here h is the mesh width and k is the degree of the (orthogonal Legendre) polynomial functions spanning the finite element subspace. The underlying temporal discretization scheme in time is the third-order total variation diminishing Runge-Kutta scheme. We justify the advantages of the Runge-Kutta discontinuous Galerkin method in a series of numerical examples.

• Investigative Magnetic Resonance Imaging
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• v.13 no.1
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• pp.22-30
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• 2009

Purpose : Patient motion during magnetic resonance (MR) imaging is one of the major problems due to its long scan time. Entropy based post-processing motion correction techniques have been shown to correct motion artifact effectively. One of main limitations of these techniques however is its long processing time. In this study, we propose several methods to reduce this long processing time effectively. Materials and Methods : To reduce the long processing time, we used the separability property of two dimensional Fourier transform (2-D FT). Also, a computationally light metric (sum of all image pixel intensity) was used instead of the entropy criterion. Finally, partial Fourier reconstruction, in particular the projection onto convex set (POCS) method, was combined thereby reducing the size of the data which should be processed and corrected. Results : Time savings of each proposed method are presented with different data size of brain images. In vivo data were processed using the proposed method and showed similar image quality. The total processing time was reduced to 15% in two dimensional images and 30% in the three dimensional images. Conclusion : The proposed methods can be useful in reducing image motion artifacts when only post-processing motion correction algorithms are available. The proposed methods can also be combined with parallel imaging technique to further reduce the processing times.

• Journal of Broadcast Engineering
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• v.8 no.1
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• pp.37-44
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• 2003

The standard approach to signal resampling is to fit the original image to a continuous model and resample the function at a desired rate. We used the compact B-spline function as the continuous model which produces less oscillatory behavior than other tails functions. In the case of nonuniform resampling based on a B-spline model, the digital signal is fitted to a spline model, and then the fitted signal is resampled at a space varying rate determined by the transformation function. It is simple to implement but may suffer from artifacts due to data loss. The main purpose of this paper is the derivation of optimal nonuniform resampling algorithm. For the optimal nonuniform formulation, the resampled signal is represented by a combination of shift varying splines determined by the transformation function. This optimal nonuniform resampling algorithm can be verified from the experiments that It produces less errors.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.325-334
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• 2006

For $f{\in}L^2(B,d{\nu})$, ${\parallel}f{\parallel}_{BMO}=\widetilde{{\mid}f{\mid}^2}(z)-{\mid}{\tilde{f}}(z){\mid}^2$. For f continuous on B, ${\parallel}f{\parallel}_{BO}=sup\{w(f)(z):z{\in}B\}$ where $w(f)(z)=sup\{{\mid}f(z)-f(w){\mid}:{\beta}(z,w){\leq}1\}$. In this paper, we will show that if $f{\in}BMO$, then ${\parallel}f{\parallel}_{BO}{\leq}M{\parallel}f{\parallel}_{BMO}$. We will also show that if $f{\in}BO$, then ${\parallel}f{\parallel}_{BMO}{\leq}M{\parallel}f{\parallel}_{BO}^2$. A homomorphic function $f:B{\rightarrow}{\mathbb{C}}$ is called a Bloch function ($f{\in}{\mathcal{B}}$) if ${\parallel}f{\parallel}_{\mathcal{B}}=sup_{z{\in}B}\;Qf(z)$<${\infty}$. In this paper, we will show that if $f{\in}{\mathcal{B}}$, then ${\parallel}f{\parallel}_{BO}{\leq}{\parallel}f{\parallel}_{\mathcal{B}}$. We will also show that if $f{\in}BMO$ and f is holomorphic, then ${\parallel}f{\parallel}_{\mathcal{B}}^2{\leq}M{\parallel}f{\parallel}_{BMO}$.