• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• 대한전기학회논문지
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• 제39권8호
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• pp.868-874
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• 1990

A singular value approach is presented in order to determine the number of multiple sinusoids from the finite noisy data. Simulations are conducted for Akaike's information criterion (AIC), Rissanen's shortest data description (MDL) and a singular value approach, for various examples with different SNR's and methods of estimating frequencies. And then the performances are compared. Simulation results that the singular value approach is superior to AIC and MDL for FBLP, HOYW and covariance matrix based methods are investigated. The approach with contribute to the frequency estimation of multiple sinusoids from the finite noisy data. Furthermore, this will be applied to the DSPs of communication and bio-medical engineering.

• 제어로봇시스템학회논문지
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• 제1권1호
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• pp.13-19
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• 1995

In this paper, generalized singular value is defined. Using the generalized singular value, robust stability conditions and robust pole placement conditions of structured uncertain systems with star shaped uncertainties are derived. Especially, norm bounded and polytopic uncertainty regions are considered as star shaped uncertainty regions. Linear matrix inequality problems are proposed in order to compute the upper bound of the generalized singular value. The proposed linear matrix inequality problems can be solved by using the convex optimization method.

• 대한수학회지
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• 제61권3호
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• pp.427-444
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• 2024

The matrix completion problem is to predict missing entries of a data matrix using the low-rank approximation of the observed entries. Typical approaches to matrix completion problem often rely on thresholding the singular values of the data matrix. However, these approaches have some limitations. In particular, a discontinuity is present near the thresholding value, and the thresholding value must be manually selected. To overcome these difficulties, we propose a shrinkage and thresholding function that smoothly thresholds the singular values to obtain more accurate and robust estimation of the data matrix. Furthermore, the proposed function is differentiable so that the thresholding values can be adaptively calculated during the iterations using Stein unbiased risk estimate. The experimental results demonstrate that the proposed algorithm yields a more accurate estimation with a faster execution than other matrix completion algorithms in image inpainting problems.

• 한국소음진동공학회논문집
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• 제11권9호
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• pp.431-438
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• 2001

This paper present experimental results of source identification for non-minimum phase system. Generally, a causal linear system may be described by matrix form. The inverse problem is considered as a matrix inversion. Direct inverse method can\`t be applied for a non-minimum phase system, the reason is that the system has ill-conditioning. Therefore, in this study to execute an effective inversion, SVD inverse technique is introduced. In a Non-minimum phase system, its system matrix may be singular or near-singular and has one more very small singular values. These very small singular values have information about a phase of the system and ill-conditioning. Using this property we could solve the ill-conditioned problem of the system and then verified it for the practical system(cantilever beam). The experimental results show that SVD inverse technique works well for non-minimum phase system.

• 대한수학회지
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• 제37권5호
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• pp.822-822
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• 2000

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권6호
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• pp.2634-2648
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• 2020

In this paper, an adaptive sparse singular value decomposition (ASSVD) algorithm is proposed to estimate the signal matrix when only one data matrix is observed and there is high dimensional white noise, in which we assume that the signal matrix is low-rank and has sparse singular vectors, i.e. it is a simultaneously low-rank and sparse matrix. It is a structured matrix since the non-zero entries are confined on some small blocks. The proposed algorithm estimates the singular values and vectors separable by exploring the structure of singular vectors, in which the recent developments in Random Matrix Theory known as anisotropic Marchenko-Pastur law are used. And then we prove that when the signal is strong in the sense that the signal to noise ratio is above some threshold, our estimator is consistent and outperforms over many state-of-the-art algorithms. Moreover, our estimator is adaptive to the data set and does not require the variance of the noise to be known or estimated. Numerical simulations indicate that ASSVD still works well when the signal matrix is not very sparse.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권2호
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• pp.883-900
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• 2017

In this paper block based blind secure gray image watermarking scheme based on discrete wavelet transform and singular value decomposition is proposed. In devising the proposed scheme, security is given high importance along with other two requirements: robustness and imperceptibility. The use of discrete wavelet transform not only improves robustness but the selection of bands with high tolerance towards noise caused an improvement in terms of imperceptibility. The robustness further improved due to the involvement of singular vectors along with singular values in watermark embedding and extraction process. Finally, to achieve security, the selected DWT band is decomposed into smaller blocks and random blocks are chosen for modification. Furthermore, the elements of left and right singular vectors of selected blocks are chosen based on their dependence upon each other for watermark embedding. Various experiments using different images as host and watermark were conducted to examine and validate the proposed technique. Additionally, the proposed technique is tested against various attacks like compression, affine transformation, cropping, translation, X shearing, scaling, Y shearing, filtering, blurring, different kinds of noises, histogram equalization, rotation, etc. Lastly, the proposed technique is compared with state-of-the-art watermarking techniques and their comparison shows significant improvement of proposed scheme over existing techniques.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2012년도 춘계학술대회 논문집
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• pp.324-329
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• 2012

Isolation tables are widely used for precision equipments and their isolation performances have been usually expressed and evaluated by transsmissibility. However, transmissibility is a concept for 1-degree of freedom(DOF) system. In practice, isolation tables are supproted by more than 4 springs. Each spring is subjected to vertical and horizontal ground vibrations, and also the table has more than 1-DOF. Therefore, isolation tables should be treated as multi-input/multi-output(MIMO) system of which isolation performance is expressed by transmissibility matrix. However, the matrix is too complicated to be an index for a system. In this paper, maximum singular value of transmissibility matrx is suggested as a simple performance index of a MIMO isolation system. Physical meaning of singular value is explained using a simple a 2-DOF isolation table. Furthermore, maximum singular values of passive, 3-DOF active and 6-DOF active isolation tables are obtained through experiments, and their meaning are explained and compared with each other.

• 인터넷정보학회논문지
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• 제24권5호
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• pp.29-35
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• 2023

CCTV는 범죄 예방, 공공 안전 강화, 교통 관리 등 다양한 목적으로 사용된다. 그러나 카메라의 범위와 해상도가 향상됨에 따라 영상에서 개인의 신상정보가 노출되는 위험성이 있다. 따라서 영상에서 개인 정보를 보호함과 동시에 개인을 식별할 수 있는 새로운 기술의 필요성이 존재한다. 본 논문에서는 객체 식별 및 추적을 위한 히스토그램 기반 특이값 분해를 제안한다. 제안하는 방법은 객체의 색상 정보를 이용하여 영상에 존재하는 서로 다른 객체를 구분한다. 객체 인식을 위하여 YOLO와 DeepSORT를 이용해 영상에 존재하는 사람을 탐지 및 추출한다. 탐지된 사람의 위치 정보를 이용해 흑백 히스토그램으로 색상 값을 추출한다. 추출한 색상 값 중 유의미한 정보만을 추출하여 사용하기 위해 특이값 분해를 이용한다. 특이값 분해를 이용할 때 결과에서 상위 특이값의 평균을 이용함으로 객체 색상 추출의 정확도를 높인다. 특이값 분해를 이용해 추출한 색상 정보를 다른 영상에 존재하는 색상과 비교하며 서로 다른 영상에 존재하는 동일 인물을 탐지한다. 색상 정보 비교를 위해 유클리드 거리를 이용하며 정확도 평가는 Top-N을 이용한다. 평가 결과 흑백 히스토그램과 특이값 분해를 사용하여 동일 인물을 탐지할 때 최대 100%에서 최소 74%를 기록하였다.