• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2017.10a
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• pp.681-683
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• 2017

In the digital information age, image processing is essential for various digital devices such as smart phones, cameras, and TVs. However, degradation occurs in analyzing, recognizing, and processing image data, and salt & pepper noise occurs. Therefore, in this paper, we applied linear interpolation method, newton interpolation method, lagrange interpolation method, and spline interpolation method to the image damaged by salt & pepper noise in order to find more effective interpolation method in salt & pepper noise environment, The methods were compared using the PSNR (peak signal to noise ratio).

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.4
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• pp.965-972
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• 2015

Along with the rapid development in digital times, image media are being used in internet, computer and digital camera. But image deterioration occurs due to various exterior reasons in the procedures of acquisition, processing, transmission and recording of digital image and major reason is noise. Therefore in order to remove salt & pepper noise, this study suggested the algorithm which replaces the noise to original pixel in case of non-noise, and processes the noise with Lagrange interpolation method in case of noise. In case high density noise was added and the noise could not be removed, noise characteristics were improved by processing the noises repeatedly. And for objective judgment, this method was compared with existing methods and PSNR(peak signal to noise ratio) was used as judgment standard.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.2
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• pp.455-462
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• 2015

Image media is used for the internet, computers and digital cameras as part of the core services of multimedia. Digital images can be easily acquired and processed, due to the development of digital home appliances and personal computers' application software. However, image degradation occurs by various external causes in the acquisition, processing and transmitting process of digital images, and its main cause is known to be noise. Therefore, this study proposed and conducted the simulation of image restoration filter algorithm that processes impulse noise and Gaussian noise by applying Lagrange interpolation and spatial weighted method according to distance, respectively. The proposed algorithm improved 8.77[dB], 8.83[dB] and 10.02[dB], respectively, compared to existing A-TMF, AWMF and MMF, as a result of processing by applying the damaged Girl images to impulse noise(P=60%) and Gaussian noise(${\sigma}=10$).

• Journal of KSNVE
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• v.5 no.4
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• pp.503-514
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• 1995

In the case of performing experimental modal analysis(EMA) and finite- element analysis(EFA) for a whole structure of automotive body that is composed of many complex parts, a trouble may arise from the calculation time, the capacity of memory in computers and the experimental conditions, etc. In this paper, for the vibrational analysis of automotive body model, the efficient modal synthesis method by means of dividing the whole structure into two parts and performing EMA and FEA for each part is studied. In addition, the method based on Lagrange interpolation is proposed for approximating rotational degrees-of-freedom information and linking FEA with EMA. In result, by measuring translational degrees-of-freedom information of only few points and adopting only few modes, the linking method based on Lagrange interpolation turned out to be efficient and accurate in the low frequency range.

• Proceedings of the KIEE Conference
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• 2005.05a
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• pp.161-163
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• 2005

In this paper, we propose an efficient motion vector recovery algorithm for the new coding standard H.264, which makes use of the Lagrange interpolation formula. In H.264/AVC, a 16$\times$16 macroblock can be divided into different block shapes for motion estimation, and each block has its own motion vector. In the natural video the motion vector is likely to move in the same direction, hence the neighboring motion vectors are correlative. Because the motion vector in H.264 covers smaller area than previous coding standards, the correlation between neighboring motion vectors increases. We can use the Lagrange interpolation formula to constitute a polynomial that describes the motion tendency of motion vectors, and use this polynomial to recover the lost motion vector. The simulation result shows that our algorithm can efficiently improve the visual quality of the corrupted video.

• ETRI Journal
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• v.6 no.2
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• pp.18-26
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• 1984

Among the various forms of interpolating polynomial for approximation, this paper is a study about the characteristics of piecewise Lagrange interpolating polynomials. And throughout the study, an attempt is made to construct the two-dimensional ap proximating function over Rectangular Grid and Triangular Grid by using the one-dim ensional interpolating polynomials.

• Proceedings of the KIEE Conference
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• 2003.07e
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• pp.55-57
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• 2003

This paper presents a new method for finding the Block Pulse series coefficients and deriving the Block Pulse integration operational matrices which are necessary for the control fields using the Block Pulse functions. In this paper, the accuracy of the Block Pulse series coefficients derived by using the Lagrange second order interpolation polynomial is approved by the mathematical method.

• Water for future
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• v.27 no.2
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• pp.155-166
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• 1994

Various Eulerian-Lagrangian numerical models for the one-dimensional longitudinal dispersion equation are studied comparatively. In the model studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing adveciton and the other dispersion. The advection equation has been solved using the method of characteristics following fluid particles along the characteristic line and the results are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpolation polynomials are superior to Lagrange interpolation polynomials in reducing dissipation and dispersion errors in the simulation.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.51 no.6
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• pp.235-240
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• 2002

This paper presents a new method for estimating the block pulse series coefficients by using the Lagrange's second order interpolation polynomial. Block pulse functions have been used in a variety of fields such as the analysis and controller design of the systems. When the block pulse functions are used, it is necessary to find the more exact value of the block pulse series coefficients. But these coefficients have been estimated by the mean of the adjacent discrete values, and the result is not sufficient when the values are changing extremely. In this paper, the method for improving the accuracy of the block pulse series coefficients by using the Lagrange's second order interpolation polynomial is presented.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.48 no.3
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• pp.119-124
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• 2011

Interpolation filters are widely used in many communication and multimedia applications. Polynomial interpolation computes the coefficients of the polynomial according to the input information to obtain the interpolated value. Recently, FIR interpolation method using supplementary filters was proposed to improve the performances of polynomial interpolation methods. In this paper, by combining a weighting factor approach with the supplementary filter method, we propose a weighted interpolation method which can be efficiently used to compute the maximum or minimum values of a given curve using only a restricted number of sample values. With application to the interpolation of normal distribution curves used in XRF systems, it is shown that the proposed approach exhibits improved performances compared with conventional interpolation methods.