• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1613-1622
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• 2008

Let G be a graph with vertex set V(G) and edge set E(G), and let g, f be two nonnegative integer-valued functions defined on V(G) such that $g(x)\;{\leq}\;f(x)$ for every vertex x of V(G). We use $d_G(x)$ to denote the degree of a vertex x of G. A (g, f)-factor of G is a spanning subgraph F of G such that $g(x)\;{\leq}\;d_F(x)\;{\leq}\;f(x)$ for every vertex x of V(F). In particular, G is called a (g, f)-graph if G itself is a (g, f)-factor. A (g, f)-factorization of G is a partition of E(G) into edge-disjoint (g, f)-factors. Let F = {$F_1$, $F_2$, ..., $F_m$} be a factorization of G and H be a subgraph of G with mr edges. If $F_i$, $1\;{\leq}\;i\;{\leq}\;m$, has exactly r edges in common with H, we say that F is r-orthogonal to H. If for any partition {$A_1$, $A_2$, ..., $A_m$} of E(H) with $|A_i|=r$ there is a (g, f)-factorization F = {$F_1$, $F_2$, ..., $F_m$} of G such that $A_i\;{\subseteq}E(F_i)$, $1\;{\leq}\;i\;{\leq}\;m$, then we say that G has (g, f)-factorizations randomly r-orthogonal to H. In this paper it is proved that every (0, mf - (m - 1)r)-graph has (0, f)-factorizations randomly r-orthogonal to any given subgraph with mr edges if $f(x)\;{\geq}\;3r\;-\;1$ for any $x\;{\in}\;V(G)$.

• Journal of Broadcast Engineering
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• v.11 no.4 s.33
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• pp.495-506
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• 2006

In this paper, we propose a self-calibration of a multi-camera system using factorization techniques for realistic contents generation. The traditional self-calibration algorithms for multi-camera systems have been focused on stereo(-rig) camera systems or multiple camera systems with a fixed configuration. Thus, it is required to exploit them in 3D reconstruction with a mobile multi-camera system and another general applications. For those reasons, we suggest the robust algorithm for general structured multi-camera systems including the algorithm for a plane-structured multi-camera system. In our paper, we explain the theoretical background and practical usages based on a projective factorization and the proposed affine factorization. We show experimental results with simulated data and real images as well. The proposed algorithm can be used for a 3D reconstruction and a mobile Augmented Reality.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.383-388
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• 2005

Depth recovery in robot vision is an essential problem to infer the three dimensional geometry of scenes from a sequence of the two dimensional images. In the past, many studies have been proposed for the depth estimation such as stereopsis, motion parallax and blurring phenomena. Among cues for depth estimation, depth from lens translation is based on shape from motion by using feature points. This approach is derived from the correspondence of feature points detected in images and performs the depth estimation that uses information on the motion of feature points. The approaches using motion vectors suffer from the occlusion or missing part problem, and the image blur is ignored in the feature point detection. This paper presents a novel approach to the defocus technique based depth from lens translation using sequential SVD factorization. Solving such the problems requires modeling of mutual relationship between the light and optics until reaching the image plane. For this mutuality, we first discuss the optical properties of a camera system, because the image blur varies according to camera parameter settings. The camera system accounts for the camera model integrating a thin lens based camera model to explain the light and optical properties and a perspective projection camera model to explain the depth from lens translation. Then, depth from lens translation is proposed to use the feature points detected in edges of the image blur. The feature points contain the depth information derived from an amount of blur of width. The shape and motion can be estimated from the motion of feature points. This method uses the sequential SVD factorization to represent the orthogonal matrices that are singular value decomposition. Some experiments have been performed with a sequence of real and synthetic images comparing the presented method with the depth from lens translation. Experimental results have demonstrated the validity and shown the applicability of the proposed method to the depth estimation.

• Journal of the Institute of Convergence Signal Processing
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• v.8 no.2
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• pp.106-112
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• 2007

This paper proposes a hybrid architecture algorithm for fast computation of DCT and DFT via recursive factorization. Recursive factorization of DCT-II and DFT transform matrix leads to a similar architectural structure so that common architectural base may be used by simply adding a switching device. Linking between two transforms was derived based on matrix recursion formula. Hybrid acrchitectural design for DCT and DFT matrix decomposition were derived using the generation matrix and the trigonometric identities and relations. Data flow diagram for high-speed architecture of Cooley-Tukey type was drawn to accommodate DCT/DFT hybrid architecture. From this data flow diagram computational complexity is comparable to that of the fast DCT algorithms for moderate size of N. Further investigation is needed for multi-mode operation use of FFT architecture in other orthogonal transform computation.

• The Journal of the Acoustical Society of Korea
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• v.37 no.6
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• pp.489-498
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• 2018

In this paper, a target detection method based on beamspace-domain multichannel nonnegative matrix factorization is studied when an echo of continuous-wave ping is received from a low-Doppler target in reverberant environment. If the receiver of the continuous-wave active sonar moves, the frequency range of the reverberation is broadened due to the Doppler effect, so the low-Doppler target echo is interfered by the reverberation in this case. The developed algorithm analyzes the multichannel spectrogram of the received signal into frequency bases, time bases, and beamformer gains using the beamspace-domain multichannel nonnnegative matrix factorization, then the algorithm estimates the frequency, time, and bearing of target echo by choosing a proper basis. To analyze the performance of the developed algorithm, simulations were performed in various signal-to-reverberation conditions. The results show that the proposed algorithm can estimate the frequency, time, and bearing, but the performance was degraded in the low signal-to-reverberation condition. It is expected that modifying the selection algorithm of the target echo basis can enhance the performance according to the simulation results.

• The Journal of the Acoustical Society of Korea
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• v.41 no.4
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• pp.468-479
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• 2022

To detect targets with active sonar system in the underwater environments, the targets are localized by receiving the echoes of the transmitted sounds reflected from the targets. In this case, reverberation from the scatterers is also generated, which prevents detection of the target echo. To detect the target effectively, reverberation suppression techniques such as pre-whitening based on autoregressive model and principal component inversion have been studied, and recently a Non-negative Matrix Factorization (NMF)-based technique has been also devised. The NMF-based reverberation suppression technique shows improved performance compared to the conventional methods, but the geometry of the transducer and receiver and attenuation by distance have not been considered. In this paper, the performance is improved through preprocessing such as the directionality of the receiver, Doppler related thereto, and attenuation for distance, in the case of using a continuous wave with a bistatic sonar. In order to evaluate the performance of the proposed system, simulation with a reverberation model was performed. The results show that the detection probability performance improved by 10 % to 40 % at a low false alarm probability of 1 % relative to the conventional non-negative matrix factorization.

• The Journal of the Acoustical Society of Korea
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• v.43 no.4
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• pp.369-382
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• 2024

To suppress the reverberation in the active sonar system, the non-negative matrix factorization-based reverberation suppression methods have been researched recently. An estimation loss function, which makes the multiplication of basis matrices same as the input signals, has to be considered to design the non-negative matrix factorization methods, but the conventional method simply chooses the Kullback-Leibler divergence asthe lossfunction without any considerations. In this paper, we examined that the Kullback-Leibler divergence is the best lossfunction or there isthe other loss function enhancing the performance. First, we derived a modified reverberation suppression algorithm using the generalized beta-divergence function, which includes the Kullback-Leibler divergence. Then, we performed Monte-Carlo simulations using synthesized reverberation for the modified reverberation suppression method. The results showed that the Kullback-Leibler divergence function (β = 1) has good performances in the high signal-to-reverberation environments, but the intermediate function (β = 1.25) between Kullback-Leibler divergence and Euclidean distance has better performance in the low signal-to-reverberation environments.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.365-380
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• 2012

Non-negative matrix factorization (NMF) is a very efficient method to explain the relationship between functions for finding basis information of multivariate nonnegative data. The multiplicative update (MU) algorithm is a popular approach to solve the NMF problem, but it fails to approach a stationary point and has inner iteration and zero divisor. So the elementwisely alternating projected gradient (eAPG) algorithm was proposed to overcome the defects. In this paper, we use the fact that the equilibrium point is stable to prove the convergence of the eAPG algorithm. By using a classic model, the equilibrium point is obtained and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the eAPG algorithm are obtained, which can accelerate the convergence. In addition, the conditions, which satisfy that the non-zero equilibrium point exists and is stable, can cause that the algorithm converges to different values. Both of them are confirmed in the experiments. And we give the mathematical proof that the eAPG algorithm can reach the appointed precision at the least iterations compared to the MU algorithm. Thus, we theoretically illustrate the advantages of the eAPG algorithm.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.12
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• pp.1152-1162
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• 2008

This paper deals with the State-Dependent Riccati Equation (SDRE) technique for the design of helicopter nonlinear flight controllers. Since the SDRE controller requires a linear system-like structure for nonlinear motion equations, a state-dependent coefficient (SDC) factorization technique is developed in order to derive the conforming structure from a general nonlinear helicopter dynamic model. Also on-line numerical methods of solving the algebraic Riccati equation are investigated to improve the numerical efficiency in designing the SDRE controllers. The proposed method is applied to trajectory tracking problems of the helicopter and computational tips for a real time application are proposed using a high fidelity rotorcraft mathematical model.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.5
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• pp.65-72
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• 1994

We resolve the suboptimal $\infty$ control problem using (J,J')-lossless coprime factorization by transforming the linear fractional transformation (LFT) into chain scattering description (CSD) in discrete-time systems. The condition transformed LFT into CSD is that the inverse matrix of $P_{21}$ of standard plant exists. But, this paper presents the method of transforming LFT into CSD for 4-block problem in case that the inverse matrix of $P_{21}$ of standard plant does not exist and parameterization of the all suboptimal $\infty$T controllers using (J,J')-lossless coprime factorization. It is shown that this method can resolve the suboptimal $\infty$ control problem solving only two Riccati equations in discrete-time systems.