• Korean Journal of Mathematics
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• v.30 no.4
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• pp.593-601
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• 2022

Let C(Q) denote Yeh-Wiener space, the space of all real-valued continuous functions x(s, t) on Q ≡ [0, S] × [0, T] with x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. For each partition τ = τ_m,n = {(s_i, t_j)|i = 1, . . . , m, j = 1, . . . , n} of Q with 0 = s₀ < s₁ < . . . < s_m = S and 0 = t₀ < t₁ < . . . < t_n = T, define a random vector X_τ : C(Q) → ℝ^mn by X_τ (x) = (x(s₁, t₁), . . . , x(s_m, t_n)). In this paper we study the conditional integral transform and the conditional convolution product for a class of cylinder type functionals defined on K(Q) with a given conditioning function X_τ above, where K(Q)is the space of all complex valued continuous functions of two variables on Q which satify x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. In particular we derive a useful equation which allows to calculate the conditional integral transform of the conditional convolution product without ever actually calculating convolution product or conditional convolution product.

• Journal of the Korean earth science society
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• v.32 no.6
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• pp.560-574
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• 2011

Satellite images that have been obtained periodically and continuously are very effective data to monitor the changes of Earth's surface. Traditionally, the studies on change detection using satellite images have mainly focused on comparison between two results after analyzing two images respectively. However, the interests in researches to catch smooth trends and short duration events from continual multi-temporal images have been increased recently. In this study, we introduce and test an approach based on 3D wavelet transform to analyze the multi-temporal satellite images. 3D wavelet transform can reduce the dimensions of data conserving main trends. Also, it is possible to extract important patterns and to analyze spatial and temporal relations with neighboring pixels using 3D wavelet transform. As a result, 3D wavelet transform is useful to capture the long term trends and short-term events rapidly. In addition, we can expect to get new information through sub-bands of 3D wavelet transform which provide different information by decomposed direction.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.7 no.7
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• pp.1575-1581
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• 2003

As a society has progressed rapidly toward a highly advanced digital information age, a multimedia communication service for acquisition, transmission and storage of image data as well as voice has being commercialized externally and internally. However, in the process of digitalization or transmission of data, noise is generated by several causes, and researches for eliminating those noises have been continued until now. There were the existing FFT(fast fourier transform) and STFT(short time fourier transform) for removing noise but it's impossible to know information about time and time-frequency localization capabilities has conflictive relationship. Therefore, for overcoming these limits, wavelet transform which is presented as a new technique of signal processing field is being applied in many fields recently. Because it has time-frequency localization capabilities it's Possible for multiresolution analysis as well as easy to analyze various signal. And when two wavelet base were designed to form Hilbert transform pair, wavelet pair provide superior performance than the existing DWT(discrete wavelet transform) in data characteristic detection. Therefore in this parer, we removed impulse noise by using adaptive-length median filter and two dyadic wavelet base which is designed by truncated coefficient vector.

• Journal of Broadcast Engineering
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• v.13 no.5
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• pp.732-743
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• 2008

In H.264/AVC, 4$\times$4 block transform is used for intra and inter prediction instead of 8$\times$8 block transform. Using small block size coding, H.264/AVC obtains high temporal prediction efficiency, however, it has limitation in utilizing spatial redundancy. Motivated on these points, we propose a multi-dimensional transform which achieves both the accuracy of temporal prediction as well as effective use of spatial redundancy. From preliminary experiments, the proposed multi-dimensional transform achieves higher energy compaction than 2-D DCT used in H.264. We designed an integer-based transform and quantization coder for multi-dimensional coder. Moreover, several additional methods for multi-dimensional coder are proposed, which are cube forming, scan order, mode decision and updating parameters. The Context-based Adaptive Variable-Length Coding (CAVLC) used in H.264 was employed for the entropy coder. Simulation results show that the performance of the multi-dimensional codec appears similar to that of H.264 in lower bit rates although the rate-distortion curves of the multi-dimensional DCT measured by entropy and the number of non-zero coefficients show remarkably higher performance than those of H.264/AVC. This implies that more efficient entropy coder optimized to the statistics of multi-dimensional DCT coefficients and rate-distortion operation are needed to take full advantage of the multi-dimensional DCT. There remains many issues and future works about multi-dimensional coder to improve coding efficiency over H.264/AVC.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2003.05a
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• pp.431-434
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• 2003

As a wavelet transform which is presented as a new technique of signal processing field has time and frequency localization capabilities, it's possible for multiresolution analysis as well as easy to analyze various signal. So it is being applied in many fields recently. And when two wavelet base were designed to form Hilbert transform pair, wavelet pair show superior performance than the existing DWT(discrete wavelet transform) in data detection of pulse type. Therefore in this paper, we detected position of impulse noise by using two dyadic wavelet base which is designed by truncated coefficient vector.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.383-395
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• 2012

In this paper, we use a computational algorithm for the inversion of the one and two-dimensional $\mathcal{L}_2$-transform based on the Bromwich's integral and the Fourier series. The new inversion formula can evaluate the inverse of the $\mathcal{L}_2$-transform with considerable accuracy over a wide range of values of the independent variable and can be devised for the functions which are not Laplace transformable and have damping motion in small interval near origin.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.9
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• pp.31-37
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• 1996

This Paper is concerned with effective signal identification method for tool breakage and micro chipping using discrete wavelet transform of feed motor current in milling operations. The wavelet transform uses an analyzing waveletfunction which is localized in both frequency and time domain to detect subtle time localized changes in input signals. The changing pattern of wavelet coefficient is continuously compared to detect tool breakage and micro chipping over one spindle revolution. The results indicate that the wavelet transform can identify tool failure with much greater sensi- tivity than the time domain monitoring and frequency domain monitoring such as FFT. Experimental results are presented to support the proposed scheme.

• IEIE Transactions on Smart Processing and Computing
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• v.5 no.5
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• pp.323-326
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• 2016

High Efficiency Video Coding (HEVC) adopts intra transform skip mode, in which a residual block is directly quantized in the pixel domain without transforming the block into the frequency domain. Intra transform skip mode provides a significant coding gain for screen content. However, when intra-prediction errors are not transformed, the errors are often correlated along the intra-prediction direction. This paper introduces a residual differential pulse code modulation (DPCM) method for the intra-predicted and transform-skipped blocks to remove redundancy. The proposed method performs pixel-by-pixel residual prediction along the intra-prediction direction to reduce the dynamic range of intra-prediction errors. Experimental results show that the transform skip mode's Bjøntegaard delta rate (BD-rate) is improved by 12.8% for vertically intra-predicted blocks. Overall, the proposed method shows an average 1.2% reduction in BD-rate, relative to HEVC, with negligible computational complexity.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10c
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• pp.509-511
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• 1998

본 논문에서는 동영상 데이터베이스에서 Key-frame을 검색하는 방법을 제안한다. 본 논문에서는 Key-frame을 검색하기위해 컬러 피쳐를 공간영역에서 추출하지 않고 wavelet transform 영역에서 컬러 피쳐를 추출하는 방법을 제안한다. wavelet transform 의 저주파 밴드는 영상전체의 특징을 잘 나타내고 고주파 밴드는 texture 와 국부적인 컬러 특성을 잘 나타낸다. 색인과정 알고리즘은 영상의 크기를 정규화하고 RGB 컬러공간에서 HSV 컬러 공간으로 변환을 하여, H, S, V 각 채널에 대해 Daubechies' wavelet transform을 수행한 후 변환 영역에서 피쳐를 추출하게 된다. 색인을 위한 피쳐로 wavelet 계수와 lowest 밴드의 평균과 표준편차를 추출하였다. 효율적인 검색을 위해 검색은 2단계로 수행된다. 먼저 평균과 표준편차만을 이용한 1차 검색을 통해 2차 검색의 후보 영상들을 추출하고 2차 검색에서는 1차 검색 통과 영상들에 대해서만 wavelet 계수들을 비교하여 최종 검색 결과를 얻게 된다. 검색결과 기존의 컬러 피쳐를 이용한 방법보다 우수한 검색결과를 얻을 수 있었다.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.571-579
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• 1999

In this paper, a Hadamard transform imaging spectrometer(HTIS) is proposed by using a grill spectrometer. And we reconfigure the system by using the grill sectrometer which uses a left cyclic S-matrix instead of the conventional right cyclic one. Then, we model the Hadamard transform imaging spectrometer and apply the mask characteristics compensation method, i.e. $ {T}^{-1}$ method, to complete fast algorithm. Also, through computer simulations the superiority of the proposed system in this paper to the conventional Hadamard transform spectrometer(HTS) is proved and the performance of the two systems are compared by introducing average mean square error(AMSE) as the algebraic criterion.