• 한국정보통신학회논문지
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• 제13권12호
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• pp.2731-2736
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• 2009

본 논문에서는 직교 기저행렬을 이용한 직교 주파수분할다중화 시스템의 새로운 구현방안이 수학적으로 개발된다. 직교기저행렬은 Haar 기저행렬을 기본으로 하고 있으나 직교 주파수분할다중화의 다중 부채널 신호를 변조하기에 적당한 형태를 갖추고 있다. 여기서는 새로운 기저행렬이 간단한 재귀알고리즘에 의하여 확장될 수 있음이 증명된다.그리고 송신기 조합행렬의 차수는 확장에 의하여 두배로 증가된다. 수신기에서 복조는 직교 기저행렬의 재귀에 의하여 생성되는 조합행렬의 역행렬에 의하여 수행된다. 따라서 제안된 직교 주파수분할다중화 시스템에서는 원 신호의 완벽한 재생이 가능함을 알 수 있다.

• 한국통신학회논문지
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• 제40권4호
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• pp.619-627
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• 2015

본 논문은 비음수 행렬 인수분해(NMF)를 이용한 음성향상 기법을 다루고 있다. 음성과 잡음에서 적절한 훈련을 통해 각각의 기저(basis) 행렬을 구하고 이 행렬들을 이용하여 두 음원을 분리 하는 것이다. 그 중에서도 음성향상의 성능은 사용하게 되는 기저 행렬에 따라 크게 달라짐을 보인다. 기존의 독립적으로 구한 음성 기저 행렬에 비해서, 잡음 데이터를 복원하는데 부적합한 방향으로 최적화시킨 음성 기저 행렬을 사용하였을 때 더 높은 음성향상 성능을 보임을 실험으로 확인하였다. 이 때 잡음 데이터의 복원 오차 자체를 크게 해주는 방향과 해당 인코딩 행렬(encoding matrix) 원소의 값을 작게 해주는 두 가지 방법을 적용하여 비교하였다. 좀 더 음성 복원에만 특화된 기저 행렬을 구함으로서 음성 기저 행렬이 잡음 데이터 복원에 사용되는 것을 최소화 하였다. 실험 결과에서는 perceptual evaluation speech quality값과 signal to distortion ratio를 지표로 사용하였고, 기존 기법에서 사용하는 기저 행렬 보다 더 높은 성능을 보임을 확인 하였다.

• ETRI Journal
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• 제30권2호
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• pp.326-334
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• 2008

This paper proposes a method for generating a basis translation matrix between isomorphic extension fields. To generate a basis translation matrix, we need the equality correspondence of a basis between the isomorphic extension fields. Consider an extension field $F_{p^m}$ where p is characteristic. As a brute force method, when $p^m$ is small, we can check the equality correspondence by using the minimal polynomial of a basis element; however, when $p^m$ is large, it becomes too difficult. The proposed methods are based on the fact that Type I and Type II optimal normal bases (ONBs) can be easily identified in each isomorphic extension field. The proposed methods efficiently use Type I and Type II ONBs and can generate a pair of basis translation matrices within 15 ms on Pentium 4 (3.6 GHz) when $mlog_2p$ = 160.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권2호
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• pp.171-188
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• 2015

In this paper, the efficient column-wise/row-wise lattice reduction (LR) updating and downdating methods are developed and their complexities are analyzed. The well-known LLL algorithm, developed by Lenstra, Lenstra, and Lov${\acute{a}}$sz, is considered as a LR method. When the column or the row is appended/deleted in the given lattice basis matrix H, the proposed updating and downdating methods modify the preconditioning matrix that is primarily computed for the LR with H and provide the initial parameters to reduce the updated lattice basis matrix efficiently. Since the modified preconditioning matrix keeps the information of the original reduced lattice bases, the redundant computational complexities can be eliminated when reducing the lattice by using the proposed methods. In addition, the rounding error analysis of the proposed methods is studied. The numerical results demonstrate that the proposed methods drastically reduce the computational load without any performance loss in terms of the condition number of the reduced lattice basis matrix.

• 대한수학회보
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• 제54권6호
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• pp.2013-2027
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• 2017

We compute explicitly the matrices represented by Toeplitz operators on the Hardy space over the unit circle with respect to a special orthonormal basis constructed by author in terms of their symbols. And we also find a necessary condition for the matrix generated by the product of two Toeplitz operators with respect to the basis to be a Toeplitz matrix by a direct calculation and we finally solve commuting problems of two Toeplitz operators in terms of symbols. This is a generalization of the classical results obtained regarding to the orthonormal basis consisting of the monomials.

• 한국통신학회논문지
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• 제19권10호
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• pp.1861-1871
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• 1994

본 논문에서는 농담구조소(濃淡構造素)(GSE, grayscale structuring element)를 갖는 형태학 필터의 실시간 처리를 위한 알고리즘을 제안하였다. 제안된 알고리즘에서는 GSE로부터 유도된 basis matrix와 입력 샘플들로 구성된 input matrix를 이용하여 각 형태학 연산들을 소역행렬연산(local matrix operation)으로 새롭게 정의하고 있는데, 이를 이용하여 opening이나 closing과 같은 복합 형태학 연산들을 실시간으로 처리할 수 있음을 보였다. 제안된 알고리즘은 복원 형태학 연산들을 erosion과 dilation의 직렬조합(cascade combination)으로 처리하던 기존의 방법에 비해 적은 메모리를 필요로 하면서도, 출력을 얻기까지의 지연(遲延)(delay)이 훨씬 적다는 장점을 갖는다. 또한 본 논문에서는 형태학 필터를 VLSI로 구현하기 위한 효율적 방안을 제안하였다. 제안된 방법에서는 p-bit으로 표현되는 신호에 대한 형태학 연산을 p개의 이진(binary) 형태학 연산자들의 조합으로 구현하였는데, 각 이진 연산자들은 MSB(most significant bit)부터 순차적으로 (bit-serial approach) 해당 레벨의 bit들을 처리하여 출력을 부를 구조로 이루어져 있다. 본 논문에서는 형태학 필터의 VLSI 구현에 있어서 제안된 방법이 기존의 Threshold Decomposition 방법 등에 비해 보다 효율적이라는 것을 보였다.

• ETRI Journal
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• 제39권6호
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• pp.841-850
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• 2017

We investigate neural network image reconstruction for magnetic particle imaging. The network performance strongly depends on the convolution effects of the spectrum input data. The larger convolution effect appearing at a relatively smaller nanoparticle size obstructs the network training. The trained single-layer network reveals the weighting matrix consisting of a basis vector in the form of Chebyshev polynomials of the second kind. The weighting matrix corresponds to an inverse system matrix, where an incoherency of basis vectors due to low convolution effects, as well as a nonlinear activation function, plays a key role in retrieving the matrix elements. Test images are well reconstructed through trained networks having an inverse kernel matrix. We also confirm that a multi-layer network with one hidden layer improves the performance. Based on the results, a neural network architecture overcoming the low incoherence of the inverse kernel through the classification property is expected to become a better tool for image reconstruction.

• 대한수학회논문집
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• 제10권4호
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• pp.849-854
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• 1995

The interpolation of scattered data with radial basis functions is knwon for its good fitting. But if data get large, the coefficient matrix becomes almost singular. We introduce different knots and nodes to improve condition number of coefficient matrix. The singulaity of new coefficient matrix is investigated here.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 1998년도 추계학술대회 논문집
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• pp.63-66
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• 1998

In the implementation of the simplex method program, the representation and the maintenance of basis matrix is very important, In the experimental study, we investigates Suhl's idea in the LU factorization and LU update of basis matrix. First, the triangularization of basis matrix is implemented and its efficiency is shown. Second, various technique in the dynamic Markowitz's ordering and threshold pivoting are presented. Third, modified Forrest-Tomlin LU update method exploiting sparsity is presented. Fourth, as a storage scheme of LU factors, Gustavson data structure is explained. Fifth, efficient timing of reinversion is developed. Finally, we show that modified Forrest-Tomlin method with Gustavson data structure is superior more than 30% to the Reid method with linked list data structure.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권2호
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• pp.107-121
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• 2016

We analyze the complexity of the LLL algorithm, invented by Lenstra, Lenstra, and $Lov{\acute{a}}sz$ as a a well-known lattice reduction (LR) algorithm which is previously known as having the complexity of $O(N^4{\log}B)$ multiplications (or, $O(N^5({\log}B)^2)$ bit operations) for a lattice basis matrix $H({\in}{\mathbb{R}}^{M{\times}N})$ where B is the maximum value among the squared norm of columns of H. This implies that the complexity of the lattice reduction algorithm depends only on the matrix size and the lattice basis norm. However, the matrix structures (i.e., the correlation among the columns) of a given lattice matrix, which is usually measured by its condition number or determinant, can affect the computational complexity of the LR algorithm. In this paper, to see how the matrix structures can affect the LLL algorithm's complexity, we derive a more tight upper bound on the complexity of LLL algorithm in terms of the condition number and determinant of a given lattice matrix. We also analyze the complexities of the LLL updating/downdating schemes using the proposed upper bound.